Operator Inequalities Of Ostrowski And Trapezoidal Type

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Operator Inequalities of Ostrowski and Trapezoidal Type

Author : Silvestru Sever Dragomir
Publisher : Springer Science & Business Media
ISBN 13 : 1461417791
Total Pages : 121 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Operator Inequalities of Ostrowski and Trapezoidal Type by : Silvestru Sever Dragomir

Download or read book Operator Inequalities of Ostrowski and Trapezoidal Type written by Silvestru Sever Dragomir and published by Springer Science & Business Media. This book was released on 2011-12-08 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inequalities of Ostrowski and Trapezoidal Type for Functions of Selfadjoint Operators on Hilbert Spaces presents recent results concerning Ostrowski and Trapezoidal type inequalities for continuous functions of bounded Selfadjoint operators on complex Hilbert spaces. The first chapter recalls some fundamental facts concerning bounded Selfadjoint operators on complex Hilbert spaces. The generalized Schwarz’s inequality for positive Selfadjoint operators as well as some results for the spectrum of this class of operators are presented. The author also introduces and explores the fundamental results for polynomials in a linear operator, continuous functions of selfadjoint operators that will play a central role throughout the book. The following chapter is devoted to the Ostrowski’s type inequalities, which provide sharp error estimates in approximating the value of a function by its integral mean and can be used to obtain a priory error bounds for different quadrature rules in approximating the Riemann integral by different Riemann sums. The author also presents recent results extending Ostrowski inequality in various directions for continuous functions of selfadjoint operators in complex Hilbert spaces. The final chapter illustrates recent results obtained in extending trapezoidal type inequality in various directions for continuous functions of selfadjoint operators in complex Hilbert spaces. Applications for mid-point inequalities and some elementary functions of operators as also provided. This book is intended for use by researchers in various fields of Linear Operator Theory and Mathematical Inequalities. As well as postgraduate students and scientists applying inequalities in their specific areas.

Operator Inequalities of Ostrowski and Trapezoidal Type

Author :
Publisher :
ISBN 13 : 9781461417804
Total Pages : 124 pages
Book Rating : 4.4/5 (178 download)

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Book Synopsis Operator Inequalities of Ostrowski and Trapezoidal Type by :

Download or read book Operator Inequalities of Ostrowski and Trapezoidal Type written by and published by . This book was released on 2011-12-09 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Handbook of Functional Equations

Author : Themistocles M. Rassias
Publisher : Springer
ISBN 13 : 1493912461
Total Pages : 555 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Handbook of Functional Equations by : Themistocles M. Rassias

Download or read book Handbook of Functional Equations written by Themistocles M. Rassias and published by Springer. This book was released on 2014-11-18 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: As Richard Bellman has so elegantly stated at the Second International Conference on General Inequalities (Oberwolfach, 1978), “There are three reasons for the study of inequalities: practical, theoretical, and aesthetic.” On the aesthetic aspects, he said, “As has been pointed out, beauty is in the eye of the beholder. However, it is generally agreed that certain pieces of music, art, or mathematics are beautiful. There is an elegance to inequalities that makes them very attractive.” The content of the Handbook focuses mainly on both old and recent developments on approximate homomorphisms, on a relation between the Hardy–Hilbert and the Gabriel inequality, generalized Hardy–Hilbert type inequalities on multiple weighted Orlicz spaces, half-discrete Hilbert-type inequalities, on affine mappings, on contractive operators, on multiplicative Ostrowski and trapezoid inequalities, Ostrowski type inequalities for the Riemann–Stieltjes integral, means and related functional inequalities, Weighted Gini means, controlled additive relations, Szasz–Mirakyan operators, extremal problems in polynomials and entire functions, applications of functional equations to Dirichlet problem for doubly connected domains, nonlinear elliptic problems depending on parameters, on strongly convex functions, as well as applications to some new algorithms for solving general equilibrium problems, inequalities for the Fisher’s information measures, financial networks, mathematical models of mechanical fields in media with inclusions and holes.

Intelligent Comparisons II: Operator Inequalities and Approximations

Author : George A. Anastassiou
Publisher : Springer
ISBN 13 : 331951475X
Total Pages : 224 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Intelligent Comparisons II: Operator Inequalities and Approximations by : George A. Anastassiou

Download or read book Intelligent Comparisons II: Operator Inequalities and Approximations written by George A. Anastassiou and published by Springer. This book was released on 2017-01-13 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This compact book focuses on self-adjoint operators’ well-known named inequalities and Korovkin approximation theory, both in a Hilbert space environment. It is the first book to study these aspects, and all chapters are self-contained and can be read independently. Further, each chapter includes an extensive list of references for further reading. The book’s results are expected to find applications in many areas of pure and applied mathematics. Given its concise format, it is especially suitable for use in related graduate classes and research projects. As such, the book offers a valuable resource for researchers and graduate students alike, as well as a key addition to all science and engineering libraries.

Applications of Nonlinear Analysis

Author : Themistocles M. Rassias
Publisher : Springer
ISBN 13 : 3319898159
Total Pages : 931 pages
Book Rating : 4.3/5 (198 download)

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Book Synopsis Applications of Nonlinear Analysis by : Themistocles M. Rassias

Download or read book Applications of Nonlinear Analysis written by Themistocles M. Rassias and published by Springer. This book was released on 2018-06-29 with total page 931 pages. Available in PDF, EPUB and Kindle. Book excerpt: New applications, research, and fundamental theories in nonlinear analysis are presented in this book. Each chapter provides a unique insight into a large domain of research focusing on functional equations, stability theory, approximation theory, inequalities, nonlinear functional analysis, and calculus of variations with applications to optimization theory. Topics include: Fixed point theory Fixed-circle theory Coupled fixed points Nonlinear duality in Banach spaces Jensen's integral inequality and applications Nonlinear differential equations Nonlinear integro-differential equations Quasiconvexity, Stability of a Cauchy-Jensen additive mapping Generalizations of metric spaces Hilbert-type integral inequality, Solitons Quadratic functional equations in fuzzy Banach spaces Asymptotic orbits in Hill’sproblem Time-domain electromagnetics Inertial Mann algorithms Mathematical modelling Robotics Graduate students and researchers will find this book helpful in comprehending current applications and developments in mathematical analysis. Research scientists and engineers studying essential modern methods and techniques to solve a variety of problems will find this book a valuable source filled with examples that illustrate concepts.

Intelligent Analysis: Fractional Inequalities and Approximations Expanded

Author : George A. Anastassiou
Publisher : Springer Nature
ISBN 13 : 3030386368
Total Pages : 525 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Intelligent Analysis: Fractional Inequalities and Approximations Expanded by : George A. Anastassiou

Download or read book Intelligent Analysis: Fractional Inequalities and Approximations Expanded written by George A. Anastassiou and published by Springer Nature. This book was released on 2020-01-15 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on computational and fractional analysis, two areas that are very important in their own right, and which are used in a broad variety of real-world applications. We start with the important Iyengar type inequalities and we continue with Choquet integral analytical inequalities, which are involved in major applications in economics. In turn, we address the local fractional derivatives of Riemann–Liouville type and related results including inequalities. We examine the case of low order Riemann–Liouville fractional derivatives and inequalities without initial conditions, together with related approximations. In the next section, we discuss quantitative complex approximation theory by operators and various important complex fractional inequalities. We also cover the conformable fractional approximation of Csiszar’s well-known f-divergence, and present conformable fractional self-adjoint operator inequalities. We continue by investigating new local fractional M-derivatives that share all the basic properties of ordinary derivatives. In closing, we discuss the new complex multivariate Taylor formula with integral remainder. Sharing results that can be applied in various areas of pure and applied mathematics, the book offers a valuable resource for researchers and graduate students, and can be used to support seminars in related fields.

Unification of Fractional Calculi with Applications

Author : George A. Anastassiou
Publisher : Springer Nature
ISBN 13 : 3030869202
Total Pages : 422 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Unification of Fractional Calculi with Applications by : George A. Anastassiou

Download or read book Unification of Fractional Calculi with Applications written by George A. Anastassiou and published by Springer Nature. This book was released on 2021-11-21 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book demonstrates the unifying methods of generalized versions of Hilfer, Prabhakar and Hilfer–Prabhakar fractional calculi, and we establish related unifying fractional integral inequalities of the following types: Iyengar, Landau, Polya, Ostrowski, Hilbert–Pachpatte, Hardy, Opial, Csiszar’s f-Divergence, self-adjoint operator and related to fuzziness. Our results are univariate and multivariate. This book’s results are expected to find applications in many areas of pure and applied mathematics, especially in fractional inequalities and fractional differential equations. Other interesting applications can be in applied sciences like geophysics, physics, chemistry, economics and engineering. This book is appropriate for researchers, graduate students, practitioners and seminars of the above disciplines, also to be in all science and engineering libraries.

Advanced Mathematical Analysis and its Applications

Author : Pradip Debnath
Publisher : CRC Press
ISBN 13 : 1000967263
Total Pages : 493 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Advanced Mathematical Analysis and its Applications by : Pradip Debnath

Download or read book Advanced Mathematical Analysis and its Applications written by Pradip Debnath and published by CRC Press. This book was released on 2023-10-17 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Mathematical Analysis and its Applications presents state-of-the-art developments in mathematical analysis through new and original contributions and surveys, with a particular emphasis on applications in engineering and mathematical sciences. New research directions are indicated in each of the chapters, and while this book is meant primarily for graduate students, there is content that will be equally useful and stimulating for faculty and researchers. The readers of this book will require minimum knowledge of real, complex, and functional analysis, and topology. Features Suitable as a reference for graduate students, researchers, and faculty Contains the most up-to-date developments at the time of writing.

Ostrowski Type Inequalities and Applications in Numerical Integration

Author : Sever S. Dragomir
Publisher : Springer Science & Business Media
ISBN 13 : 9401725195
Total Pages : 491 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Ostrowski Type Inequalities and Applications in Numerical Integration by : Sever S. Dragomir

Download or read book Ostrowski Type Inequalities and Applications in Numerical Integration written by Sever S. Dragomir and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: It was noted in the preface of the book "Inequalities Involving Functions and Their Integrals and Derivatives", Kluwer Academic Publishers, 1991, by D.S. Mitrinovic, J.E. Pecaric and A.M. Fink; since the writing of the classical book by Hardy, Littlewood and Polya (1934), the subject of differential and integral inequalities has grown by about 800%. Ten years on, we can confidently assert that this growth will increase even more significantly. Twenty pages of Chapter XV in the above mentioned book are devoted to integral inequalities involving functions with bounded derivatives, or, Ostrowski type inequalities. This is now itself a special domain of the Theory of Inequalities with many powerful results and a large number of applications in Numerical Integration, Probability Theory and Statistics, Information Theory and Integral Operator Theory. The main aim of the present book, jointly written by the members of the Vic toria University node of RGMIA (Research Group in Mathematical Inequali ties and Applications, http: I /rgmia. vu. edu. au) and Th. M. Rassias, is to present a selected number of results on Ostrowski type inequalities. Results for univariate and multivariate real functions and their natural applications in the error analysis of numerical quadrature for both simple and multiple integrals as well as for the Riemann-Stieltjes integral are given.

Mathematical Analysis and Applications

Author : Michael Ruzhansky
Publisher : John Wiley & Sons
ISBN 13 : 1119414334
Total Pages : 1050 pages
Book Rating : 4.1/5 (194 download)

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Book Synopsis Mathematical Analysis and Applications by : Michael Ruzhansky

Download or read book Mathematical Analysis and Applications written by Michael Ruzhansky and published by John Wiley & Sons. This book was released on 2018-04-11 with total page 1050 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields.

Approximation Theory and Analytic Inequalities

Author : Themistocles M. Rassias
Publisher : Springer Nature
ISBN 13 : 3030606228
Total Pages : 546 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Approximation Theory and Analytic Inequalities by : Themistocles M. Rassias

Download or read book Approximation Theory and Analytic Inequalities written by Themistocles M. Rassias and published by Springer Nature. This book was released on 2021-07-21 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume focuses on various important areas of mathematics in which approximation methods play an essential role. It features cutting-edge research on a wide spectrum of analytic inequalities with emphasis on differential and integral inequalities in the spirit of functional analysis, operator theory, nonlinear analysis, variational calculus, featuring a plethora of applications, making this work a valuable resource. The reader will be exposed to convexity theory, polynomial inequalities, extremal problems, prediction theory, fixed point theory for operators, PDEs, fractional integral inequalities, multidimensional numerical integration, Gauss–Jacobi and Hermite–Hadamard type inequalities, Hilbert-type inequalities, and Ulam’s stability of functional equations. Contributions have been written by eminent researchers, providing up-to-date information and several results which may be useful to a wide readership including graduate students and researchers working in mathematics, physics, economics, operational research, and their interconnections.

Mathematical Inequalities

Author : Pietro Cerone
Publisher : CRC Press
ISBN 13 : 1439848971
Total Pages : 391 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Mathematical Inequalities by : Pietro Cerone

Download or read book Mathematical Inequalities written by Pietro Cerone and published by CRC Press. This book was released on 2010-12-01 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Drawing on the authors' research work from the last ten years, Mathematical Inequalities: A Perspective gives readers a different viewpoint of the field. It discusses the importance of various mathematical inequalities in contemporary mathematics and how these inequalities are used in different applications, such as scientific modeling.The authors

Advanced Inequalities

Author : George A Anastassiou
Publisher : World Scientific
ISBN 13 : 9814464341
Total Pages : 424 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Advanced Inequalities by : George A Anastassiou

Download or read book Advanced Inequalities written by George A Anastassiou and published by World Scientific. This book was released on 2010-10-26 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents univariate and multivariate classical analyses of advanced inequalities. This treatise is a culmination of the author's last thirteen years of research work. The chapters are self-contained and several advanced courses can be taught out of this book. Extensive background and motivations are given in each chapter with a comprehensive list of references given at the end.The topics covered are wide-ranging and diverse. Recent advances on Ostrowski type inequalities, Opial type inequalities, Poincare and Sobolev type inequalities, and Hardy-Opial type inequalities are examined. Works on ordinary and distributional Taylor formulae with estimates for their remainders and applications as well as Chebyshev-Gruss, Gruss and Comparison of Means inequalities are studied.The results presented are mostly optimal, that is the inequalities are sharp and attained. Applications in many areas of pure and applied mathematics, such as mathematical analysis, probability, ordinary and partial differential equations, numerical analysis, information theory, etc., are explored in detail, as such this monograph is suitable for researchers and graduate students. It will be a useful teaching material at seminars as well as an invaluable reference source in all science libraries.

Probabilistic Inequalities

Author :
Publisher :
ISBN 13 : 9814467138
Total Pages : pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Probabilistic Inequalities by :

Download or read book Probabilistic Inequalities written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Intelligent Comparisons: Analytic Inequalities

Author : George A. Anastassiou
Publisher : Springer
ISBN 13 : 3319211218
Total Pages : 662 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Intelligent Comparisons: Analytic Inequalities by : George A. Anastassiou

Download or read book Intelligent Comparisons: Analytic Inequalities written by George A. Anastassiou and published by Springer. This book was released on 2015-07-11 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents recent and original work of the author on inequalities in real, functional and fractional analysis. The chapters are self-contained and can be read independently, they include an extensive list of references per chapter. The book’s results are expected to find applications in many areas of applied and pure mathematics, especially in ordinary and partial differential equations and fractional differential equations. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, as well as Science and Engineering University libraries.

New Perspectives on the Theory of Inequalities for Integral and Sum

Author : Nazia Irshad
Publisher : Springer Nature
ISBN 13 : 3030905632
Total Pages : 319 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis New Perspectives on the Theory of Inequalities for Integral and Sum by : Nazia Irshad

Download or read book New Perspectives on the Theory of Inequalities for Integral and Sum written by Nazia Irshad and published by Springer Nature. This book was released on 2022-03-29 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides new contributions to the theory of inequalities for integral and sum, and includes four chapters. In the first chapter, linear inequalities via interpolation polynomials and green functions are discussed. New results related to Popoviciu type linear inequalities via extension of the Montgomery identity, the Taylor formula, Abel-Gontscharoff's interpolation polynomials, Hermite interpolation polynomials and the Fink identity with Green’s functions, are presented. The second chapter is dedicated to Ostrowski’s inequality and results with applications to numerical integration and probability theory. The third chapter deals with results involving functions with nondecreasing increments. Real life applications are discussed, as well as and connection of functions with nondecreasing increments together with many important concepts including arithmetic integral mean, wright convex functions, convex functions, nabla-convex functions, Jensen m-convex functions, m-convex functions, m-nabla-convex functions, k-monotonic functions, absolutely monotonic functions, completely monotonic functions, Laplace transform and exponentially convex functions, by using the finite difference operator of order m. The fourth chapter is mainly based on Popoviciu and Cebysev-Popoviciu type identities and inequalities. In this last chapter, the authors present results by using delta and nabla operators of higher order.

Riemann–Stieltjes Integral Inequalities for Complex Functions Defined on Unit Circle

Author : Silvestru Sever Dragomir
Publisher : CRC Press
ISBN 13 : 1000566676
Total Pages : 47 pages
Book Rating : 4.0/5 (5 download)

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Book Synopsis Riemann–Stieltjes Integral Inequalities for Complex Functions Defined on Unit Circle by : Silvestru Sever Dragomir

Download or read book Riemann–Stieltjes Integral Inequalities for Complex Functions Defined on Unit Circle written by Silvestru Sever Dragomir and published by CRC Press. This book was released on 2019-08-19 with total page 47 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main aim of this book is to present several results related to functions of unitary operators on complex Hilbert spaces obtained, by the author in a sequence of recent research papers. The fundamental tools to obtain these results are provided by some new Riemann-Stieltjes integral inequalities of continuous integrands on the complex unit circle and integrators of bounded variation. Features All the results presented are completely proved and the original references where they have been firstly obtained are mentioned Intended for use by both researchers in various fields of Linear Operator Theory and Mathematical Inequalities, as well as by postgraduate students and scientists applying inequalities in their specific areas Provides new emphasis to mathematical inequalities, approximation theory and numerical analysis in a simple, friendly and well-digested manner. About the Author Silvestru Sever Dragomir is Professor and Chair of Mathematical Inequalities at the College of Engineering & Science, Victoria University, Melbourne, Australia. He is the author of many research papers and several books on Mathematical Inequalities and their Applications. He also chairs the international Research Group in Mathematical Inequalities and Applications (RGMIA). For details, see https://rgmia.org/index.php.