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Inequalities Involving Functions And Their Integrals And Derivatives
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Author :Dragoslav S. Mitrinovic Publisher :Springer Science & Business Media ISBN 13 :9401135622 Total Pages :602 pages Book Rating :4.4/5 (11 download)
Book Synopsis Inequalities Involving Functions and Their Integrals and Derivatives by : Dragoslav S. Mitrinovic
Download or read book Inequalities Involving Functions and Their Integrals and Derivatives written by Dragoslav S. Mitrinovic and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: One service mathematics has rendered the ~l moil ..., Ii j'avait su comment en revenir, je n'y serais point aUe.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'(ftre of this series.
Book Synopsis Differential and Integral Inequalities by : Dorin Andrica
Download or read book Differential and Integral Inequalities written by Dorin Andrica and published by Springer Nature. This book was released on 2019-11-14 with total page 848 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theories, methods and problems in approximation theory and analytic inequalities with a focus on differential and integral inequalities are analyzed in this book. Fundamental and recent developments are presented on the inequalities of Abel, Agarwal, Beckenbach, Bessel, Cauchy–Hadamard, Chebychev, Markov, Euler’s constant, Grothendieck, Hilbert, Hardy, Carleman, Landau–Kolmogorov, Carlson, Bernstein–Mordell, Gronwall, Wirtinger, as well as inequalities of functions with their integrals and derivatives. Each inequality is discussed with proven results, examples and various applications. Graduate students and advanced research scientists in mathematical analysis will find this reference essential to their understanding of differential and integral inequalities. Engineers, economists, and physicists will find the highly applicable inequalities practical and useful to their research.
Book Synopsis Integral Inequalities and Applications by : D.D. Bainov
Download or read book Integral Inequalities and Applications written by D.D. Bainov and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to integral inequalities of the Gronwall-Bellman-Bihari type. Following a systematic exposition of linear and nonlinear inequalities, attention is paid to analogues including integro-differential inequalities, functional differential inequalities, and discrete and abstract analogues. Applications to the investigation of the properties of solutions of various classes of equations such as uniqueness, stability, dichotomy, asymptotic equivalence and behaviour is also discussed. The book comprises three chapters. Chapter I and II consider classical linear and nonlinear integral inequalities. Chapter III is devoted to various classes of integral inequalities of Gronwall type, and their analogues, which find applications in the theory of integro-differential equations, partial differential equations, differential equations with deviating argument, impube differential equations, etc. Each chapter concludes with a section illustrating the manner of application. The book also contains an extensive bibliography. For researchers whose work involves the theory and application of integral inequalities in mathematics, engineering and physics.
Book Synopsis Mathematical Constants by : Steven R. Finch
Download or read book Mathematical Constants written by Steven R. Finch and published by Cambridge University Press. This book was released on 2003-08-18 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. This book is helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example, combinatorial enumeration or geometric optimization. Unsolved problems appear virtually everywhere as well. This work represents an outstanding scholarly attempt to bring together all significant mathematical constants in one place.
Book Synopsis Integral and Discrete Inequalities and Their Applications by : Yuming Qin
Download or read book Integral and Discrete Inequalities and Their Applications written by Yuming Qin and published by Birkhäuser. This book was released on 2016-10-06 with total page 1072 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concentrates on one- and multi-dimensional nonlinear integral and discrete Gronwall-Bellman type inequalities. It complements the author’s book on linear inequalities and serves as an essential tool for researchers interested in differential (ODE and PDE), difference, and integral equations. The present volume is part 2 of the author’s two-volume work on inequalities. Integral and discrete inequalities are a very important tool in classical analysis and play a crucial role in establishing the well-posedness of the related equations, i.e., differential, difference and integral equations.
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.
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.
Book Synopsis On Extended Hardy-hilbert Integral Inequalities And Applications by : Bicheng Yang
Download or read book On Extended Hardy-hilbert Integral Inequalities And Applications written by Bicheng Yang and published by World Scientific. This book was released on 2023-02-13 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert-type inequalities, including Hilbert's inequalities proved in 1908, Hardy-Hilbert-type inequalities proved in 1934, and Yang-Hilbert-type inequalities first proved around 1998, play an important role in analysis and its applications. These inequalities are mainly divided in three classes: integral, discrete and half-discrete. During the last twenty years, there have been many research advances on Hilbert-type inequalities, and especially on Yang-Hilbert-type inequalities.In the present monograph, applying weight functions, the idea of parametrization as well as techniques of real analysis and functional analysis, we prove some new Hilbert-type integral inequalities as well as their reverses with parameters. These inequalities constitute extensions of the well-known Hardy-Hilbert integral inequality. The equivalent forms and some equivalent statements of the best possible constant factors associated with several parameters are considered. Furthermore, we also obtain the operator expressions with the norm and some particular inequalities involving the Riemann-zeta function and the Hurwitz-zeta function. In the form of applications, by means of the beta function and the gamma function, we use the extended Hardy-Hilbert integral inequalities to consider several Hilbert-type integral inequalities involving derivative functions and upper limit functions. In the last chapter, we consider the case of Hardy-type integral inequalities. The lemmas and theorems within provide an extensive account of these kinds of integral inequalities and operators.Efforts have been made for this monograph hopefully to be useful, especially to graduate students of mathematics, physics and engineering, as well as researchers in these domains.
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:
Book Synopsis Recent Progress in Inequalities by : G.V. Milovanovic
Download or read book Recent Progress in Inequalities written by G.V. Milovanovic and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the late Professor Dragoslav S. Mitrinovic(1908-1995), one of the most accomplished masters in the domain of inequalities. Inequalities are to be found everywhere and play an important and significant role in almost all subjects of mathematics as well as in other areas of sciences. Professor Mitrinovic used to say: `There are no equalities, even in human life inequalities are always encountered.' This volume provides an extensive survey of the most current topics in almost all subjects in the field of inequalities, written by 85 outstanding scientists from twenty countries. Some of the papers were presented at the International Memorial Conference dedicated to Professor D.S. Mitrinovic, which was held at the University of Nis, June 20-22, 1996. Audience: This book will be of great interest to researchers in real, complex and functional analysis, special functions, approximation theory, numerical analysis and computation, and other fields, as well as to graduate students requiring the most up-to-date results.
Book Synopsis On Hilbert-Type and Hardy-Type Integral Inequalities and Applications by : Bicheng Yang
Download or read book On Hilbert-Type and Hardy-Type Integral Inequalities and Applications written by Bicheng Yang and published by Springer Nature. This book was released on 2019-09-25 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed toward graduate students and researchers in mathematics, physics and engineering interested in the latest developments in analytic inequalities, Hilbert-Type and Hardy-Type integral inequalities, and their applications. Theories, methods, and techniques of real analysis and functional analysis are applied to equivalent formulations of Hilbert-type inequalities, Hardy-type integral inequalities as well as their parameterized reverses. Special cases of these integral inequalities across an entire plane are considered and explained. Operator expressions with the norm and some particular analytic inequalities are detailed through several lemmas and theorems to provide an extensive account of inequalities and operators.
Book Synopsis Differential and Integral Inequalities: Theory and Applications by : V. Lakshmikantham
Download or read book Differential and Integral Inequalities: Theory and Applications written by V. Lakshmikantham and published by Academic Press. This book was released on 1969 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume constitutes the first part of a monograph on theory and applications of differential and integral inequalities. 'The entire work, as a whole, is intended to be a research monograph, a guide to the literature, and a textbook for advanced courses. The unifying theme of this treatment is a systematic development of the theory and applications of differential inequalities as well as Volterra integral inequalities. The main tools for applications are the norm and the Lyapunov functions. Familiarity with real and complex analysis, elements of general topology and functional analysis, and differential and integral equations is assumed.
Book Synopsis A Dictionary of Inequalities by : Peter Bullen
Download or read book A Dictionary of Inequalities written by Peter Bullen and published by CRC Press. This book was released on 1998-08-21 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The literature on inequalities is vast-in recent years the number of papers as well as the number of journals devoted to the subject have increased dramatically. At best, locating a particular inequality within the literature can be a cumbersome task. A Dictionary of Inequalities ends the dilemma of where to turn to find a result, a related inequality, or the references to the information you need. It provides a concise, alphabetical listing of each inequality-by its common name or its subject-with a short statement of the result, some comments, references to related inequalities, and a list of sources for further information. The author uses only the most elementary of mathematical terminology and does not offer proofs, thus making an interest in inequalities the only prerequisite for using the text. The author focuses on intuitive, physical forms of inequalities rather than their most general versions, and retains the beauty and importance of original versions rather than listing their later, abstract forms. He presents each in its simplest form with other renditions, such as for complex numbers and vectors, as extensions or under different headings. He has kept the book to a more manageable size by omitting inequalities in areas-such as elementary geometric and trigonometric inequalities-rarely used outside their fields. The end result is a current, concise, reference that puts the essential results on inequalities within easy reach. A Dictionary of Inequalities carries the beauty and attraction of the best and most successful dictionaries: on looking up a given item, the reader is likely to be intrigued and led by interest to others.
Book Synopsis Multidimensional Integral Equations and Inequalities by : B.G. Pachpatte
Download or read book Multidimensional Integral Equations and Inequalities written by B.G. Pachpatte and published by Springer Science & Business Media. This book was released on 2011-07-26 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since from more than a century, the study of various types of integral equations and inequalities has been focus of great attention by many researchers, interested both in theory and its applications. In particular, there exists a very rich literature related to the integral equations and inequalities and their applications. The present monograph is an attempt to organize recent progress related to the Multidimensional integral equations and inequalities, which we hope will widen the scope of their new applications. The field to be covered is extremely wide and it is nearly impossible to treat all of them here. The material included in the monograph is recent and hard to find in other books. It is accessible to any reader with reasonable background in real analysis and acquaintance with its related areas. All results are presented in an elementary way and the book could also serve as a textbook for an advanced graduate course. The book deserves a warm welcome to those who wish to learn the subject and it will also be most valuable as a source of reference in the field. It will be an invaluable reading for mathematicians, physicists and engineers and also for graduate students, scientists and scholars wishing to keep abreast of this important area of research.
Book Synopsis Opial Inequalities with Applications in Differential and Difference Equations by : R.P. Agarwal
Download or read book Opial Inequalities with Applications in Differential and Difference Equations written by R.P. Agarwal and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1960 the Polish mathematician Zdzidlaw Opial (1930--1974) published an inequality involving integrals of a function and its derivative. This volume offers a systematic and up-to-date account of developments in Opial-type inequalities. The book presents a complete survey of results in the field, starting with Opial's landmark paper, traversing through its generalizations, extensions and discretizations. Some of the important applications of these inequalities in the theory of differential and difference equations, such as uniqueness of solutions of boundary value problems, and upper bounds of solutions are also presented. This book is suitable for graduate students and researchers in mathematical analysis and applications.
Book Synopsis Norm Inequalities for Derivatives and Differences by : Man K. Kwong
Download or read book Norm Inequalities for Derivatives and Differences written by Man K. Kwong and published by Springer. This book was released on 2006-11-15 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: Norm inequalities relating (i) a function and two of its derivatives and (ii) a sequence and two of its differences are studied. Detailed elementary proofs of basic inequalities are given. These are accessible to anyone with a background of advanced calculus and a rudimentary knowledge of the Lp and lp spaces. The classical inequalities associated with the names of Landau, Hadamard, Hardy and Littlewood, Kolmogorov, Schoenberg and Caravetta, etc., are discussed, as well as their discrete analogues and weighted versions. Best constants and the existence and nature of extremals are studied and many open questions raised. An extensive list of references is provided, including some of the vast Soviet literature on this subject.
Book Synopsis Analytic Inequalities by : B.G. Pachpatte
Download or read book Analytic Inequalities written by B.G. Pachpatte and published by Springer Science & Business Media. This book was released on 2012-01-05 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: For more than a century, the study of various types of inequalities has been the focus of great attention by many researchers, interested both in the theory and its applications. In particular, there exists a very rich literature related to the well known Cebysev, Gruss, Trapezoid, Ostrowski, Hadamard and Jensen type inequalities. The present monograph is an attempt to organize recent progress related to the above inequalities, which we hope will widen the scope of their applications. The field to be covered is extremely wide and it is impossible to treat all of these here. The material included in the monograph is recent and hard to find in other books. It is accessible to any reader with a reasonable background in real analysis and an acquaintance with its related areas. All results are presented in an elementary way and the book could also serve as a textbook for an advanced graduate course. The book deserves a warm welcome to those who wish to learn the subject and it will also be most valuable as a source of reference in the field. It will be invaluable reading for mathematicians and engineers and also for graduate students, scientists and scholars wishing to keep abreast of this important area of research.
