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Dynamic Inequalities On Time Scales

2014-10-30 Mathematics
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Release : 2014-10-30
Genre : Mathematics
Kind : eBook
Book Rating : 020/5 ( reviews)

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Book Synopsis Dynamic Inequalities On Time Scales by : Ravi Agarwal

Download or read book Dynamic Inequalities On Time Scales written by Ravi Agarwal. This book was released on 2014-10-30. Available in PDF, EPUB and Kindle. Book excerpt: This is a monograph devoted to recent research and results on dynamic inequalities on time scales. The study of dynamic inequalities on time scales has been covered extensively in the literature in recent years and has now become a major sub-field in pure and applied mathematics. In particular, this book will cover recent results on integral inequalities, including Young's inequality, Jensen's inequality, Holder's inequality, Minkowski's inequality, Steffensen's inequality, Hermite-Hadamard inequality and Čebyšv's inequality. Opial type inequalities on time scales and their extensions with weighted functions, Lyapunov type inequalities, Halanay type inequalities for dynamic equations on time scales, and Wirtinger type inequalities on time scales and their extensions will also be discussed here in detail.

Dynamic Equations on Time Scales

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 019/5 ( reviews)

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Book Synopsis Dynamic Equations on Time Scales by : Martin Bohner

Download or read book Dynamic Equations on Time Scales written by Martin Bohner. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: On becoming familiar with difference equations and their close re lation to differential equations, I was in hopes that the theory of difference equations could be brought completely abreast with that for ordinary differential equations. [HUGH L. TURRITTIN, My Mathematical Expectations, Springer Lecture Notes 312 (page 10), 1973] A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both. [E. T. BELL, Men of Mathematics, Simon and Schuster, New York (page 13/14), 1937] The theory of time scales, which has recently received a lot of attention, was introduced by Stefan Hilger in his PhD thesis [159] in 1988 (supervised by Bernd Aulbach) in order to unify continuous and discrete analysis. This book is an intro duction to the study of dynamic equations on time scales. Many results concerning differential equations carryover quite easily to corresponding results for difference equations, while other results seem to be completely different in nature from their continuous counterparts. The study of dynamic equations on time scales reveals such discrepancies, and helps avoid proving results twice, once for differential equa tions and once for difference equations. The general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so-called time scale, which is an arbitrary nonempty closed subset of the reals.

Stability Theory for Dynamic Equations on Time Scales

2016-09-22 Mathematics
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Release : 2016-09-22
Genre : Mathematics
Kind : eBook
Book Rating : 138/5 ( reviews)

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Book Synopsis Stability Theory for Dynamic Equations on Time Scales by : Anatoly A. Martynyuk

Download or read book Stability Theory for Dynamic Equations on Time Scales written by Anatoly A. Martynyuk. This book was released on 2016-09-22. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a first in the world to present three approaches for stability analysis of solutions of dynamic equations. The first approach is based on the application of dynamic integral inequalities and the fundamental matrix of solutions of linear approximation of dynamic equations. The second is based on the generalization of the direct Lyapunovs method for equations on time scales, using scalar, vector and matrix-valued auxiliary functions. The third approach is the application of auxiliary functions (scalar, vector, or matrix-valued ones) in combination with differential dynamic inequalities. This is an alternative comparison method, developed for time continuous and time discrete systems.In recent decades, automatic control theory in the study of air- and spacecraft dynamics and in other areas of modern applied mathematics has encountered problems in the analysis of the behavior of solutions of time continuous-discrete linear and/or nonlinear equations of perturbed motion. In the book “Men of Mathematics,” 1937, E.T.Bell wrote: “A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both.”Mathematical analysis on time scales accomplishes exactly this. This research has potential applications in such areas as theoretical and applied mechanics, neurodynamics, mathematical biology and finance among others.

Hardy Type Inequalities on Time Scales

2016-10-20 Mathematics
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Release : 2016-10-20
Genre : Mathematics
Kind : eBook
Book Rating : 996/5 ( reviews)

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Book Synopsis Hardy Type Inequalities on Time Scales by : Ravi P. Agarwal

Download or read book Hardy Type Inequalities on Time Scales written by Ravi P. Agarwal. This book was released on 2016-10-20. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to dynamic inequalities of Hardy type and extensions and generalizations via convexity on a time scale T. In particular, the book contains the time scale versions of classical Hardy type inequalities, Hardy and Littlewood type inequalities, Hardy-Knopp type inequalities via convexity, Copson type inequalities, Copson-Beesack type inequalities, Liendeler type inequalities, Levinson type inequalities and Pachpatte type inequalities, Bennett type inequalities, Chan type inequalities, and Hardy type inequalities with two different weight functions. These dynamic inequalities contain the classical continuous and discrete inequalities as special cases when T = R and T = N and can be extended to different types of inequalities on different time scales such as T = hN, h > 0, T = qN for q > 1, etc.In this book the authors followed the history and development of these inequalities. Each section in self-contained and one can see the relationship between the time scale versions of the inequalities and the classical ones. To the best of the authors’ knowledge this is the first book devoted to Hardy-typeinequalities and their extensions on time scales.

Functional Dynamic Equations on Time Scales

2019-05-03 Mathematics
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Release : 2019-05-03
Genre : Mathematics
Kind : eBook
Book Rating : 203/5 ( reviews)

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Book Synopsis Functional Dynamic Equations on Time Scales by : Svetlin G. Georgiev

Download or read book Functional Dynamic Equations on Time Scales written by Svetlin G. Georgiev. This book was released on 2019-05-03. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the qualitative theory of functional dynamic equations on time scales, providing an overview of recent developments in the field as well as a foundation to time scales, dynamic systems, and functional dynamic equations. It discusses functional dynamic equations in relation to mathematical physics applications and problems, providing useful tools for investigation for oscillations and nonoscillations of the solutions of functional dynamic equations on time scales. Practice problems are presented throughout the book for use as a graduate-level textbook and as a reference book for specialists of several disciplines, such as mathematics, physics, engineering, and biology.

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