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Integral and Discrete Inequalities and Their Applications

Author : Yuming Qin

Publisher : Birkhäuser

Page : 1083 pages

File Size : 28,73 MB

Release : 2016-10-06

Category : Mathematics

ISBN : 3319333046

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Book Description

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.



Integral Inequalities and Applications

Author : D.D. Bainov

Publisher : Springer Science & Business Media

Page : 254 pages

File Size : 44,68 MB

Release : 2013-04-18

Category : Mathematics

ISBN : 9401580340

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Book Description

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.



Inequalities Involving Functions and Their Integrals and Derivatives

Author : Dragoslav S. Mitrinovic

Publisher : Springer Science & Business Media

Page : 606 pages

File Size : 44,72 MB

Release : 1991-07-31

Category : Mathematics

ISBN : 9780792313304

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Book Description

This volume provides a comprehensive, up-to-date survey of inequalities that involve a relationship between a function and its derivatives or integrals. The book is divided into 18 chapters, some of which are devoted to specific inequalities such as those of Kolmogorov-Landau, Wirtinger, Hardy, Carlson, Hilbert, Caplygin, Lyapunov, Gronwell and others. Over 800 references to the literature are cited; proofs are given when these provide insight into the general methods involved; and applications, especially to the theory of differential equations, are mentioned when appropriate. This volume will interest all those whose work involves differential and integral equations. It can also be recommended as a supplementary text.



On Hilbert-Type and Hardy-Type Integral Inequalities and Applications

Author : Bicheng Yang

Publisher : Springer Nature

Page : 152 pages

File Size : 31,6 MB

Release : 2019-09-25

Category : Mathematics

ISBN : 3030292681

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Book Description

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.



Differential and Integral Inequalities

Author : Dorin Andrica

Publisher : Springer Nature

Page : 848 pages

File Size : 22,93 MB

Release : 2019-11-14

Category : Mathematics

ISBN : 3030274071

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Book Description

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.



A Kind of Half-Discrete Hardy-Hilbert-Type Inequalities Involving Several Applications

Author : CV-Bicheng Yang

Publisher : Scientific Research Publishing, Inc. USA

Page : 189 pages

File Size : 11,86 MB

Release : 2023-12-22

Category : Antiques & Collectibles

ISBN : 1649977778

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Book Description

In this book, applying the weight functions, the idea of introduced parameters and the techniques of real analysis and functional analysis, we provide a new kind of half-discrete Hilbert-type inequalities named in Mulholland-type inequality. Then, we consider its several applications involving the derivative function of higher-order or the multiple upper limit function. Some new reverses with the partial sums are obtained. We also consider some half-discrete Hardy-Hilbert’s inequalities with two internal variables involving one derivative function or one upper limit function in the last chapter. The lemmas and theorems provide an extensive account of these kinds of half-discrete inequalities and operators.



Some Gronwall Type Inequalities and Applications

Author : Sever Silvestru Dragomir

Publisher :

Page : 210 pages

File Size : 15,32 MB

Release : 2003

Category : Mathematics

ISBN :

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Book Description

Gronwall type integral inequalities of one variable for real functions play a very important role in the Qualitative Theory of Differential Equations. The main aim of the present research monograph is to present some natural applications of Gronwall inequalities with non-linear kernels of Lipschitz type of the problems of boundedness and convergence to zero at infinity of the solutions of certain Volterra integral equations. Stability, uniform stability, uniform asymptotic stability and global asymptotic stability properties for trivial solution of certain differential system of equations are also investigated. Contents: Preface; Integral Inequalities of Gronwall Type; Inequalities for Kernels of (L)-Type; Applications to Integral Equations; Applications to Differential Equations; Index.



Recent Advances In Applied Nonlinear Dynamics With Numerical Analysis: Fractional Dynamics, Network Dynamics, Classical Dynamics And Fractal Dynamics With Their Numerical Simulations

Author : Changpin Li

Publisher : World Scientific

Page : 414 pages

File Size : 40,60 MB

Release : 2013-01-11

Category : Mathematics

ISBN : 981443647X

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Book Description

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.



Inequalities Involving Functions and Their Integrals and Derivatives

Author : Dragoslav S. Mitrinovic

Publisher : Springer Science & Business Media

Page : 602 pages

File Size : 33,6 MB

Release : 2012-12-06

Category : Mathematics

ISBN : 9401135622

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Book Description

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.



Inequalities for Finite Difference Equations

Author : B.G. Pachpatte

Publisher : CRC Press

Page : 546 pages

File Size : 17,59 MB

Release : 2001-12-13

Category : Mathematics

ISBN : 9780824706579

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Book Description

"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."