Download or read book Opial s Inequality on Time Scales and an Application written by Tamara Vernee Gray and published by . This book was released on 2007 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: Author's abstract: In view of the recently developed theory of calculus for dynamic equations on time scales (which unifies discrete and continuous systems), in this project we give some basic Opial type dynamic Inequalities. We discuss the background developed for Opial Inequalities which have many important applications both in the continuous and discrete cases in many areas of applicable analysis. Finally, having the above developed tools at our disposal, we give an example that concerns upper bound estimates of Dynamic Initial Value Problems and illustrate the usage of the developed Dynamic Opial Inequality.
Download or read book Dynamic Inequalities On Time Scales written by Ravi Agarwal and published by Springer. This book was released on 2014-10-30 with total page 264 pages. 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.
Download or read book Dynamic Equations on Time Scales and Applications written by Ravi P Agarwal and published by CRC Press. This book was released on 2024-10-18 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Integral Inequalities on Time Scales written by Svetlin G. Georgiev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-08-24 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to recent developments of linear and nonlinear integral inequalities on time scales. The book is intended for the use in the field of dynamic calculus on time scales, dynamic equation and integral equations on time scales. It is also suitable for graduate courses in the above fields. The book is designed for those who have mathematical background on time scales calculus.
Download or read book Dynamic Calculus and Equations on Time Scales written by Svetlin G. Georgiev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-09-18 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynamic Equations on Time Scales written by Martin Bohner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 365 pages. 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.
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.
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 1083 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.
Download or read book Lyapunov Inequalities and Applications written by Ravi P. Agarwal and published by Springer Nature. This book was released on 2021-04-12 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an extensive survey on Lyapunov-type inequalities. It summarizes and puts order into a vast literature available on the subject, and sketches recent developments in this topic. In an elegant and didactic way, this work presents the concepts underlying Lyapunov-type inequalities, covering how they developed and what kind of problems they address. This survey starts by introducing basic applications of Lyapunov’s inequalities. It then advances towards even-order, odd-order, and higher-order boundary value problems; Lyapunov and Hartman-type inequalities; systems of linear, nonlinear, and quasi-linear differential equations; recent developments in Lyapunov-type inequalities; partial differential equations; linear difference equations; and Lyapunov-type inequalities for linear, half-linear, and nonlinear dynamic equations on time scales, as well as linear Hamiltonian dynamic systems. Senior undergraduate students and graduate students of mathematics, engineering, and science will benefit most from this book, as well as researchers in the areas of ordinary differential equations, partial differential equations, difference equations, and dynamic equations. Some background in calculus, ordinary and partial differential equations, and difference equations is recommended for full enjoyment of the content.
Download or read book Probabilistic Inequalities written by George A Anastassiou and published by World Scientific. This book was released on 2009-08-11 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, the author presents univariate and multivariate probabilistic inequalities with coverage on basic probabilistic entities like expectation, variance, moment generating function and covariance. These are built on the recent classical form of real analysis inequalities which are also discussed in full details. This treatise is the culmination and crystallization of the author's last two decades of research work in related discipline. Each of the chapters is self-contained and a few advanced courses can be taught out of this book. Extensive background and motivations for specific topics are given in each chapter. A very extensive list of references is also provided at the end.The topics covered in this unique book are wide-ranging and diverse. The opening chapters examine the probabilistic Ostrowski type inequalities, and various related ones, as well as the largely discusses about the Grothendieck type probabilistic inequalities. The book is also about inequalities in information theory and the Csiszar's f-Divergence between probability measures. A great section of the book is also devoted to the applications in various directions of Geometry Moment Theory. Also, the development of the Grüss type and Chebyshev-Grüss type inequalities for Stieltjes integrals and the applications in probability are explored in detail. The final chapters discuss the important real analysis methods with potential applications to stochastics. The book will be of interest to researchers and graduate students, and it is also seen as an invaluable reference book to be acquired by all science libraries as well as seminars that conduct discussions on related topics.
Download or read book Hardy Type Inequalities on Time Scales written by Ravi P. Agarwal and published by Springer. This book was released on 2016-10-20 with total page 309 pages. 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.
Download or read book Intelligent Mathematics Computational Analysis written by George A. Anastassiou and published by Springer Science & Business Media. This book was released on 2011-03-19 with total page 793 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knowledge can be modeled and computed using computational mathematical methods, then lead to real world conclusions. The strongly related to that Computational Analysis is a very large area with lots of applications. This monograph includes a great variety of topics of Computational Analysis. We present: probabilistic wavelet approximations, constrained abstract approximation theory, shape preserving weighted approximation, non positive approximations to definite integrals, discrete best approximation, approximation theory of general Picard singular operators including global smoothness preservation property, fractional singular operators. We also deal with non-isotropic general Picard singular multivariate operators and q-Gauss-Weierstrass singular q-integral operators. We talk about quantitative approximations by shift-invariant univariate and multivariate integral operators, nonlinear neural networks approximation, convergence with rates of positive linear operators, quantitative approximation by bounded linear operators, univariate and multivariate quantitative approximation by stochastic positive linear operators on univariate and multivariate stochastic processes. We further present right fractional calculus and give quantitative fractional Korovkin theory of positive linear operators. We also give analytical inequalities, fractional Opial inequalities, fractional identities and inequalities regarding fractional integrals. We further deal with semi group operator approximation, simultaneous Feller probabilistic approximation. We also present Fuzzy singular operator approximations. We give transfers from real to fuzzy approximation and talk about fuzzy wavelet and fuzzy neural networks approximations, fuzzy fractional calculus and fuzzy Ostrowski inequality. We talk about discrete fractional calculus, nabla discrete fractional calculus and inequalities. We study the q-inequalities, and q-fractional inequalities. We further study time scales: delta and nabla approaches, duality principle and inequalities. We introduce delta and nabla time scales fractional calculus and inequalities. We finally study convergence with rates of approximate solutions to exact solution of multivariate Dirichlet problem and multivariate heat equation, and discuss the uniqueness of solution of general evolution partial differential equation \ in multivariate time. The exposed results are expected to find applications to: applied and computational mathematics, stochastics, engineering, artificial intelligence, vision, complexity and machine learning. This monograph is suitable for graduate students and researchers.
Download or read book Advances On Fractional Dynamic Inequalities On Time Scales written by Svetlin G Georgiev and published by World Scientific. This book was released on 2023-08-29 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Fractional Differential Equations Inclusions and Inequalities with Applications written by Sotiris K. Ntouyas and published by MDPI. This book was released on 2020-11-09 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Ostrowski and Gr ss Inequalities on Time Scales written by Thomas Matthews and published by . This book was released on 2007 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: "In this paper, a new approach in mathematics is applied to some basic inequalities in discrete and continuous analysis. The method of using time scales unifies both cases. A short introduction to the theory of time scales is given. Following this primary overview, the Montgomery identity is shown and used to derive the Ostrowski inequality on time scales, which holds in general and weighted versions. Next, the Grüss inequality is generalized on time scales. Applications will be deduced from the established theorems for discrete, continuous and q-time scale. Finally, our results are compared to the ones found in the literature. Most of the achieved formulas and statements will correspond exactly with the previously mentioned cases. Nevertheless there will be some differences in the formulation of the theorems as well as proofs"--Abstract, leaf iii.
Download or read book Issues in Logic Operations and Computational Mathematics and Geometry 2011 Edition written by and published by ScholarlyEditions. This book was released on 2012-01-09 with total page 1531 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Logic, Operations, and Computational Mathematics and Geometry. The editors have built Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Logic, Operations, and Computational Mathematics and Geometry in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Download or read book Frontiers in Time Scales and Inequalities written by George A. Anastassiou and published by World Scientific Publishing Company. This book was released on 2016 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph contains the author's work of the last four years in discrete and fractional analysis. It introduces the right delta and right nabla fractional calculus on time scales and continues with the right delta and right nabla discrete fractional calculus in the Caputo sense. Then, it shows representation formulae of functions on time scales and presents Ostrowski type inequalities, Landau type inequalities, Grüss type and comparison of means inequalities, all these over time scales. The volume continues with integral operator inequalities and their multivariate vectorial versions using convexity of functions, again all these over time scales. It follows the Grüss and Ostrowski type inequalities involving s-convexity of functions; and also examines the general case when several functions are involved. Then, it presents the general fractional Hermite-Hadamard type inequalities using m-convexity and (s, m)-convexity. Finally, it introduces the reduction method in fractional calculus and its connection to fractional Ostrowski type inequalities is studied.This book's results are expected to find applications in many areas of pure and applied mathematics, especially in difference equations and fractional differential equations. The chapters are self-contained and can be read independently, and advanced courses can be taught out of it. It is suitable for researchers, graduate students, seminars of the above subjects, and serves well as an invaluable resource for all science libraries.
