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Integral And Finite Difference Inequalities And Applications
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Book Synopsis Integral and Finite Difference Inequalities and Applications by : B. G. Pachpatte
Download or read book Integral and Finite Difference Inequalities and Applications written by B. G. Pachpatte and published by Elsevier. This book was released on 2006-09-14 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: The monograph is written with a view to provide basic tools for researchers working in Mathematical Analysis and Applications, concentrating on differential, integral and finite difference equations. It contains many inequalities which have only recently appeared in the literature and which can be used as powerful tools and will be a valuable source for a long time to come. It is self-contained and thus should be useful for those who are interested in learning or applying the inequalities with explicit estimates in their studies. Contains a variety of inequalities discovered which find numerous applications in various branches of differential, integral and finite difference equations Valuable reference for someone requiring results about inequalities for use in some applications in various other branches of mathematics Highlights pure and applied mathematics and other areas of science and technology
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 2016-10-08 with total page 989 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on one- and multi-dimensional linear integral and discrete Gronwall-Bellman type inequalities. It provides a useful collection and systematic presentation of known and new results, as well as many applications to differential (ODE and PDE), difference, and integral equations. With this work the author fills a gap in the literature on inequalities, offering an ideal source for researchers in these topics. The present volume is part 1 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 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 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 Inequalities for Finite Difference Equations by : B.G. Pachpatte
Download or read book Inequalities for Finite Difference Equations written by B.G. Pachpatte and published by CRC Press. This book was released on 2001-12-13 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A treatise on finite difference ineuqalities that have important applications to theories of various classes of finite difference and sum-difference equations, including several linear and nonlinear finite difference inequalities appearing for the first time in book form."
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 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 Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities by : Bashir Ahmad
Download or read book Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities written by Bashir Ahmad and published by Springer. This book was released on 2017-03-16 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the recent development of fractional differential equations, integro-differential equations, and inclusions and inequalities involving the Hadamard derivative and integral. Through a comprehensive study based in part on their recent research, the authors address the issues related to initial and boundary value problems involving Hadamard type differential equations and inclusions as well as their functional counterparts. The book covers fundamental concepts of multivalued analysis and introduces a new class of mixed initial value problems involving the Hadamard derivative and Riemann-Liouville fractional integrals. In later chapters, the authors discuss nonlinear Langevin equations as well as coupled systems of Langevin equations with fractional integral conditions. Focused and thorough, this book is a useful resource for readers and researchers interested in the area of fractional calculus.
Book Synopsis Recent Advances in Applied Nonlinear Dynamics with Numerical Analysis by : Changpin Li
Download or read book Recent Advances in Applied Nonlinear Dynamics with Numerical Analysis written by Changpin Li and published by World Scientific. This book was released on 2013-01-11 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear dynamics is still a hot and challenging topic. In this edited book, we focus on fractional dynamics, infinite dimensional dynamics defined by the partial differential equation, network dynamics, fractal dynamics, and their numerical analysis and simulation. Fractional dynamics is a new topic in the research field of nonlinear dynamics which has attracted increasing interest due to its potential applications in the real world, such as modeling memory processes and materials. In this part, basic theory for fractional differential equations and numerical simulations for these equations will be introduced and discussed. In the infinite dimensional dynamics part, we emphasize on numerical calculation and theoretical analysis, including constructing various numerical methods and computing the corresponding limit sets, etc. In the last part, we show interest in network dynamics and fractal dynamics together with numerical simulations as well as their applications. Contents:Gronwall Inequalities (Fanhai Zeng, Jianxiong Cao and Changpin Li)Existence and Uniqueness of the Solutions to the Fractional Differential Equations (Yutian Ma, Fengrong Zhang and Changpin Li)Finite Element Methods for Fractional Differential Equations (Changpin Li and Fanhai Zeng)Fractional Step Method for the Nonlinear Conservation Laws with Fractional Dissipation (Can Li and Weihua Deng)Error Analysis of Spectral Method for the Space and Time Fractional Fokker–Planck Equation (Tinggang Zhao and Haiyan Xuan)A Discontinuous Finite Element Method for a Type of Fractional Cauchy Problem (Yunying Zheng)Asymptotic Analysis of a Singularly Perturbed Parabolic Problem in a General Smooth Domain (Yu-Jiang Wu, Na Zhang and Lun-Ji Song)Incremental Unknowns Methods for the ADI and ADSI Schemes (Ai-Li Yang, Yu-Jiang Wu and Zhong-Hua Yang)Stability of a Collocated FV Scheme for the 3D Navier–Stokes Equations (Xu Li and Shu-qin Wang)Computing the Multiple Positive Solutions to p–Henon Equation on the Unit Square (Zhaoxiang Li and Zhonghua Yang)Multilevel WBIUs Methods for Reaction–Diffusion Equations (Yang Wang, Yu-Jiang Wu and Ai-Li Yang)Models and Dynamics of Deterministically Growing Networks (Weigang Sun, Jingyuan Zhang and Guanrong Chen)On Different Approaches to Synchronization of Spatiotemporal Chaos in Complex Networks (Yuan Chai and Li-Qun Chen)Chaotic Dynamical Systems on Fractals and Their Applications to Image Encryption (Ruisong Ye, Yuru Zou and Jian Lu)Planar Crystallographic Symmetric Tiling Patterns Generated From Invariant Maps (Ruisong Ye, Haiying Zhao and Yuanlin Ma)Complex Dynamics in a Simple Two-Dimensional Discrete System (Huiqing Huang and Ruisong Ye)Approximate Periodic Solutions of Damped Harmonic Oscillators with Delayed Feedback (Qian Guo)The Numerical Methods in Option Pricing Problem (Xiong Bo)Synchronization and Its Control Between Two Coupled Networks (Yongqing Wu and Minghai Lü) Readership: Senior undergraduates, postgraduates and experts in nonlinear dynamics with numerical analysis. Keywords:Fractional Dynamics;Infinite Dimensional Dynamics;Network Dynamics;Fractal DynamicsKey Features:The topics in this edited book are very hot and highly impressiveIssues and methods of such topics in this edited book have not been made available yetThe present edited book is suitable for various levels of researchers, such as senior undergraduates, postgraduates, and experts
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 Advances in Mathematical Inequalities and Applications by : Praveen Agarwal
Download or read book Advances in Mathematical Inequalities and Applications written by Praveen Agarwal and published by Springer. This book was released on 2018-12-31 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of original research and survey articles on mathematical inequalities and their numerous applications in diverse areas of mathematics and engineering. It includes chapters on convexity and related concepts; inequalities for mean values, sums, functions, operators, functionals, integrals and their applications in various branches of mathematics and related sciences; fractional integral inequalities; and weighted type integral inequalities. It also presents their wide applications in biomathematics, boundary value problems, mechanics, queuing models, scattering, and geomechanics in a concise, but easily understandable way that makes the further ramifications and future directions clear. The broad scope and high quality of the contributions make this book highly attractive for graduates, postgraduates and researchers. All the contributing authors are leading international academics, scientists, researchers and scholars.
Book Synopsis Regularity of Difference Equations on Banach Spaces by : Ravi P. Agarwal
Download or read book Regularity of Difference Equations on Banach Spaces written by Ravi P. Agarwal and published by Springer. This book was released on 2014-06-13 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work introduces readers to the topic of maximal regularity for difference equations. The authors systematically present the method of maximal regularity, outlining basic linear difference equations along with relevant results. They address recent advances in the field, as well as basic semi group and cosine operator theories in the discrete setting. The authors also identify some open problems that readers may wish to take up for further research. This book is intended for graduate students and researchers in the area of difference equations, particularly those with advance knowledge of and interest in functional analysis.
Book Synopsis Inequalities for Differential and Integral Equations by :
Download or read book Inequalities for Differential and Integral Equations written by and published by Elsevier. This book was released on 1997-11-12 with total page 623 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inequalities for Differential and Integral Equations has long been needed; it contains material which is hard to find in other books. Written by a major contributor to the field, this comprehensive resource contains many inequalities which have only recently appeared in the literature and which can be used as powerful tools in the development of applications in the theory of new classes of differential and integral equations. For researchers working in this area, it will be a valuable source of reference and inspiration. It could also be used as the text for an advanced graduate course. Covers a variety of linear and nonlinear inequalities which find widespread applications in the theory of various classes of differential and integral equations Contains many inequalities which have only recently appeared in literature and cannot yet be found in other books Provides a valuable reference to engineers and graduate students
Book Synopsis Differential and integral inequalities; theory and applications PART B: Functional, partial, abstract, and complex differential equations by : Lakshmikantham
Download or read book Differential and integral inequalities; theory and applications PART B: Functional, partial, abstract, and complex differential equations written by Lakshmikantham and published by Academic Press. This book was released on 1969 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential and integral inequalities; theory and applications PART B: Functional, partial, abstract, and complex differential equations
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 by :
Download or read book Differential and Integral Inequalities written by and published by . This book was released on 1969 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 2011 with total page 423 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 HardyOpial type inequalities are examined. Works on ordinary and distributional Taylor formulae with estimates for their remainders and applications as well as ChebyshevGruss, 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.
