Hardy Type Inequalities On Time Scales

Author : Ravi P. Agarwal,Donal O'Regan,Samir H. Saker
Publisher : Springer
Page : 305 pages
File Size : 53,7 Mb
Release : 2016-10-20
Category : Mathematics
ISBN : 9783319442990

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Hardy Type Inequalities on Time Scales by Ravi P. Agarwal,Donal O'Regan,Samir H. Saker Pdf

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.

Author : B. Opic,A. Kufner
Publisher : Unknown
Page : 351 pages
File Size : 44,8 Mb
Release : 1990-01-01
Category : Electronic
ISBN : 060803598X

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Hardy-Type Inequalities by B. Opic,A. Kufner Pdf

Author : Svetlin G. Georgiev
Publisher : Walter de Gruyter GmbH & Co KG
Page : 370 pages
File Size : 49,7 Mb
Release : 2023-09-18
Category : Mathematics
ISBN : 9783111185194

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Dynamic Calculus and Equations on Time Scales by Svetlin G. Georgiev Pdf

Author : Ravi P Agarwal,Bipan Hazarika,Sanket Tikare
Publisher : CRC Press
Page : 435 pages
File Size : 42,6 Mb
Release : 2024-10-18
Category : Mathematics
ISBN : 9781040103739

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Dynamic Equations on Time Scales and Applications by Ravi P Agarwal,Bipan Hazarika,Sanket Tikare Pdf

This book presents the theory of dynamic equations on time scales and applications, providing an overview of recent developments in the foundations of the field as well as its applications. It discusses the recent results related to the qualitative properties of solutions like existence and uniqueness, stability, continuous dependence, controllability, oscillations, etc. Presents cutting-edge research trends of dynamic equations and recent advances in contemporary research on the topic of time scales Connects several new areas of dynamic equations on time scales with applications in different fields Includes mathematical explanation from the perspective of existing knowledge of dynamic equations on time scales Offers several new recently developed results, which are useful for the mathematical modeling of various phenomena Useful for several interdisciplinary fields like economics, biology, and population dynamics from the perspective of new trends The text is for postgraduate students, professionals, and academic researchers working in the fields of Applied Mathematics

Author : Svetlin G Georgiev,Khaled Zennir
Publisher : World Scientific
Page : 337 pages
File Size : 55,7 Mb
Release : 2023-08-29
Category : Mathematics
ISBN : 9789811275487

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Advances On Fractional Dynamic Inequalities On Time Scales by Svetlin G Georgiev,Khaled Zennir Pdf

This book is devoted on recent developments of linear and nonlinear fractional Riemann-Liouville and Caputo integral inequalities on time scales. The book is intended for the use in the field of fractional dynamic calculus on time scales and fractional dynamic equations on time scales. It is also suitable for graduate courses in the above fields, and contains ten chapters. The aim of this book is to present a clear and well-organized treatment of the concept behind the development of mathematics as well as solution techniques. The text material of this book is presented in a readable and mathematically solid format.

Author : Ravi Agarwal,Donal O'Regan,Samir Saker
Publisher : Springer
Page : 264 pages
File Size : 44,8 Mb
Release : 2014-10-30
Category : Mathematics
ISBN : 9783319110028

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Dynamic Inequalities On Time Scales by Ravi Agarwal,Donal O'Regan,Samir Saker Pdf

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.

Author : Martin Bohner,Allan Peterson
Publisher : Springer Science & Business Media
Page : 365 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461202011

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Dynamic Equations on Time Scales by Martin Bohner,Allan Peterson Pdf

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.

Author : Alois Kufner,Lars Erik Persson
Publisher : World Scientific
Page : 380 pages
File Size : 51,9 Mb
Release : 2003
Category : Mathematics
ISBN : 9812381953

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Weighted Inequalities of Hardy Type by Alois Kufner,Lars Erik Persson Pdf

Inequalities play an important role in almost all branches of mathematics as well as in other areas of science and engineering. This book surveys the present state of the theory of weighted integral inequalities of Hardy type, including modifications concerning Hardy-Steklov operators, and some basic results about Hardy type inequalities and their limit (Carleman-Knopp type) inequalities. It also describes some rather new fields such as higher order and fractional order Hardy type inequalities and integral inequalities on the cone of monotone functions together with some applications and open problems. The book can serve as a reference and a source of inspiration for researchers working in these and related areas, but could also be used for advanced graduate courses.

Author : Bicheng Yang,Jianquan Liao
Publisher : Scientific Research Publishing, Inc. USA
Page : 410 pages
File Size : 41,7 Mb
Release : 2020-09-25
Category : Antiques & Collectibles
ISBN : 9781618969491

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Hilbert-Type Inequalities: Operators, Compositions and Extensions by Bicheng Yang,Jianquan Liao Pdf

Hilbert-type inequalities include Hilbert's inequalities, Hardy-Hilbert-type inequalities and Yang-Hilbert-type inequalities, which are important in Analysis and its applications.They are mainly divided three kinds of integral, discrete and half-discrete.In recent twenty years, there are many advances in research on Hilbert-type inequalities,especially in Yang-Hilbert-type inequalities. In this book, by using the way of weight functions, the parameterized idea and technique of Real and Functional Analysis, we introduce multi-parameters and provide three kinds of double Hilbert-type inequalities with the general measurable kernels and the best possible constant factors. The equivalent forms, the reverses and some particular inequalities are obtained. Furthermore, the operator expressions with the norm, a large number of examples on the norm, some composition formulas of the operators, and three kinds of compositional inequalities with the best possible constant factors are considered. The theory of double Hilbert-type inequalities and operators are almost built. The lemmas and theorems provide an extensive account of these kinds of inequalities and operators.

Author : CV-Bicheng Yang
Publisher : Scientific Research Publishing, Inc. USA
Page : 189 pages
File Size : 54,7 Mb
Release : 2023-12-22
Category : Antiques & Collectibles
ISBN : 9781649977779

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A Kind of Half-Discrete Hardy-Hilbert-Type Inequalities Involving Several Applications by CV-Bicheng Yang Pdf

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.

Author : Sotiris K. Ntouyas
Publisher : MDPI
Page : 518 pages
File Size : 46,8 Mb
Release : 2020-11-09
Category : Mathematics
ISBN : 9783039432189

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Fractional Differential Equations, Inclusions and Inequalities with Applications by Sotiris K. Ntouyas Pdf

During the last decade, there has been an increased interest in fractional differential equations, inclusions, and inequalities, as they play a fundamental role in the modeling of numerous phenomena, in particular, in physics, biomathematics, blood flow phenomena, ecology, environmental issues, viscoelasticity, aerodynamics, electrodynamics of complex medium, electrical circuits, electron-analytical chemistry, control theory, etc. This book presents collective works published in the recent Special Issue (SI) entitled "Fractional Differential Equation, Inclusions and Inequalities with Applications" of the journal Mathematics. This Special Issue presents recent developments in the theory of fractional differential equations and inequalities. Topics include but are not limited to the existence and uniqueness results for boundary value problems for different types of fractional differential equations, a variety of fractional inequalities, impulsive fractional differential equations, and applications in sciences and engineering.

Author : Chao Wang,Ravi P. Agarwal
Publisher : Springer Nature
Page : 443 pages
File Size : 52,9 Mb
Release : 2022-09-22
Category : Mathematics
ISBN : 9783031116193

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Combined Measure and Shift Invariance Theory of Time Scales and Applications by Chao Wang,Ravi P. Agarwal Pdf

This monograph is devoted to developing a theory of combined measure and shift invariance of time scales with the related applications to shift functions and dynamic equations. The study of shift closeness of time scales is significant to investigate the shift functions such as the periodic functions, the almost periodic functions, the almost automorphic functions, and their generalizations with many relevant applications in dynamic equations on arbitrary time scales. First proposed by S. Hilger, the time scale theory—a unified view of continuous and discrete analysis—has been widely used to study various classes of dynamic equations and models in real-world applications. Measure theory based on time scales, in its turn, is of great power in analyzing functions on time scales or hybrid domains. As a new and exciting type of mathematics—and more comprehensive and versatile than the traditional theories of differential and difference equations—, the time scale theory can precisely depict the continuous-discrete hybrid processes and is an optimal way forward for accurate mathematical modeling in applied sciences such as physics, chemical technology, population dynamics, biotechnology, and economics and social sciences. Graduate students and researchers specializing in general dynamic equations on time scales can benefit from this work, fostering interest and further research in the field. It can also serve as reference material for undergraduates interested in dynamic equations on time scales. Prerequisites include familiarity with functional analysis, measure theory, and ordinary differential equations.

Author : Alois Kufner,Lech Maligranda,Lars-Erik Persson
Publisher : Unknown
Page : 161 pages
File Size : 55,6 Mb
Release : 2007
Category : Electronic
ISBN : 8086843157

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The Hardy Inequality by Alois Kufner,Lech Maligranda,Lars-Erik Persson Pdf

Author : Michael Ruzhansky,Durvudkhan Suragan
Publisher : Springer
Page : 579 pages
File Size : 47,7 Mb
Release : 2019-07-02
Category : Mathematics
ISBN : 9783030028954

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Hardy Inequalities on Homogeneous Groups by Michael Ruzhansky,Durvudkhan Suragan Pdf

This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding.

Author : Martin Bohner,Allan C. Peterson
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 45,7 Mb
Release : 2011-06-28
Category : Mathematics
ISBN : 9780817682309

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Advances in Dynamic Equations on Time Scales by Martin Bohner,Allan C. Peterson Pdf

Excellent introductory material on the calculus of time scales and dynamic equations.; Numerous examples and exercises illustrate the diverse application of dynamic equations on time scales.; Unified and systematic exposition of the topics allows good transitions from chapter to chapter.; Contributors include Anderson, M. Bohner, Davis, Dosly, Eloe, Erbe, Guseinov, Henderson, Hilger, Hilscher, Kaymakcalan, Lakshmikantham, Mathsen, and A. Peterson, founders and leaders of this field of study.; Useful as a comprehensive resource of time scales and dynamic equations for pure and applied mathematicians.; Comprehensive bibliography and index complete this text.