Advances In Inequalities For Special Functions

Author : Pietro Cerone,Sever Silvestru Dragomir
Publisher : Unknown
Page : 186 pages
File Size : 51,6 Mb
Release : 2008
Category : Mathematics
ISBN : UOM:39015073949516

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Advances in Inequalities for Special Functions by Pietro Cerone,Sever Silvestru Dragomir Pdf

This book is the first in a collection of research monographs that are devoted to presenting recent research, development and use of Mathematical Inequalities for Special Functions. All the papers incorporated in the book have peen peer-reviewed and cover a range of topics that include both survey material of previously published works as well as new results. In his presentation on special functions approximations and bounds via integral representation, Pietro Cerone utilises the classical Stevensen inequality and bounds for the Ceby sev functional to obtain bounds for some classical special functions. The methodology relies on determining bounds on integrals of products of functions. The techniques are used to obtain novel and useful bounds for the Bessel function of the first kind, the Beta function, the Zeta function and Mathieu series.

Author : George A Anastassiou
Publisher : World Scientific
Page : 424 pages
File Size : 43,6 Mb
Release : 2010-10-26
Category : Mathematics
ISBN : 9789814464345

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Advanced Inequalities by George A Anastassiou Pdf

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 Hardy-Opial type inequalities are examined. Works on ordinary and distributional Taylor formulae with estimates for their remainders and applications as well as Chebyshev-Gruss, 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.

Author : Praveen Agarwal,Silvestru Sever Dragomir,Mohamed Jleli,Bessem Samet
Publisher : Springer
Page : 349 pages
File Size : 40,5 Mb
Release : 2018-12-31
Category : Mathematics
ISBN : 9789811330131

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Advances in Mathematical Inequalities and Applications by Praveen Agarwal,Silvestru Sever Dragomir,Mohamed Jleli,Bessem Samet Pdf

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.

Author : G.V. Milovanovic
Publisher : Springer Science & Business Media
Page : 518 pages
File Size : 51,5 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401590860

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Recent Progress in Inequalities by G.V. Milovanovic Pdf

This volume is dedicated to the late Professor Dragoslav S. Mitrinovic(1908-1995), one of the most accomplished masters in the domain of inequalities. Inequalities are to be found everywhere and play an important and significant role in almost all subjects of mathematics as well as in other areas of sciences. Professor Mitrinovic used to say: `There are no equalities, even in human life inequalities are always encountered.' This volume provides an extensive survey of the most current topics in almost all subjects in the field of inequalities, written by 85 outstanding scientists from twenty countries. Some of the papers were presented at the International Memorial Conference dedicated to Professor D.S. Mitrinovic, which was held at the University of Nis, June 20-22, 1996. Audience: This book will be of great interest to researchers in real, complex and functional analysis, special functions, approximation theory, numerical analysis and computation, and other fields, as well as to graduate students requiring the most up-to-date results.

Author : Sever Silvestru Dragomir,Anthony Sofo
Publisher : Nova Publishers
Page : 252 pages
File Size : 40,7 Mb
Release : 2008
Category : Mathematics
ISBN : 1600219209

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Advances in Inequalities for Series by Sever Silvestru Dragomir,Anthony Sofo Pdf

This research monograph, deals with identities and inequalities relating to series and their application. This is the first volume of research monographs on advances in inequalities for series. All of the papers in this volume have been fully peer reviewed. Some papers in this volume appear in print for the first time, detailing many technical results and some other papers offer a review of a number of recently published results. The papers appear in author alphabetical order and not in mathematics subject classification. There are fifteen diverse papers in this volume each with its own speciality. An important issue in many applications of Probability Theory is finding an approximate measure of distance, or discrimination, between two probability distributions. A number of divergence measures for this purpose have been proposed.

Author : Shigeru Furuichi
Publisher : Walter de Gruyter GmbH & Co KG
Page : 267 pages
File Size : 53,8 Mb
Release : 2020-01-20
Category : Mathematics
ISBN : 9783110643473

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Advances in Mathematical Inequalities by Shigeru Furuichi Pdf

Mathematical inequalities are essential tools in mathematics, natural science and engineering. This book gives an overview on recent advances. Some generalizations and improvements for the classical and well-known inequalities are described. They will be applied and further developed in many fields. Applications of the inequalities to entropy theory and quantum physics are also included.

Author : George A. Anastassiou
Publisher : World Scientific
Page : 423 pages
File Size : 41,9 Mb
Release : 2011
Category : Mathematics
ISBN : 9789814317627

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Advanced Inequalities by George A. Anastassiou Pdf

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.

Author : B.G. Pachpatte
Publisher : Springer Science & Business Media
Page : 310 pages
File Size : 52,9 Mb
Release : 2012-01-05
Category : Mathematics
ISBN : 9789491216442

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Analytic Inequalities by B.G. Pachpatte Pdf

For more than a century, the study of various types of inequalities has been the focus of great attention by many researchers, interested both in the theory and its applications. In particular, there exists a very rich literature related to the well known Cebysev, Gruss, Trapezoid, Ostrowski, Hadamard and Jensen type inequalities. The present monograph is an attempt to organize recent progress related to the above inequalities, which we hope will widen the scope of their applications. The field to be covered is extremely wide and it is impossible to treat all of these here. The material included in the monograph is recent and hard to find in other books. It is accessible to any reader with a reasonable background in real analysis and an 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 invaluable reading for mathematicians and engineers and also for graduate students, scientists and scholars wishing to keep abreast of this important area of research.

Author : Shigeru Furuichi
Publisher : Walter de Gruyter GmbH & Co KG
Page : 344 pages
File Size : 55,9 Mb
Release : 2020-01-20
Category : Mathematics
ISBN : 9783110643640

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Advances in Mathematical Inequalities by Shigeru Furuichi Pdf

Mathematical inequalities are essential tools in mathematics, natural science and engineering. This book gives an overview on recent advances. Some generalizations and improvements for the classical and well-known inequalities are described. They will be applied and further developed in many fields. Applications of the inequalities to entropy theory and quantum physics are also included.

Author : Dragoslav S. Mitrinovic,J. Pecaric,V. Volenec
Publisher : Springer Science & Business Media
Page : 728 pages
File Size : 55,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401578424

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Recent Advances in Geometric Inequalities by Dragoslav S. Mitrinovic,J. Pecaric,V. Volenec Pdf

Author : Lynn Harold Loomis,Shlomo Sternberg
Publisher : World Scientific Publishing Company
Page : 596 pages
File Size : 42,6 Mb
Release : 2014-02-26
Category : Mathematics
ISBN : 9789814583954

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Advanced Calculus by Lynn Harold Loomis,Shlomo Sternberg Pdf

An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

Author : CV-Bicheng Yang
Publisher : Scientific Research Publishing, Inc. USA
Page : 189 pages
File Size : 43,8 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 : A.A. Gonchar,E.B. Saff
Publisher : Springer Science & Business Media
Page : 463 pages
File Size : 47,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461229667

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Progress in Approximation Theory by A.A. Gonchar,E.B. Saff Pdf

Designed to give a contemporary international survey of research activities in approximation theory and special functions, this book brings together the work of approximation theorists from North America, Western Europe, Asia, Russia, the Ukraine, and several other former Soviet countries. Contents include: results dealing with q-hypergeometric functions, differencehypergeometric functions and basic hypergeometric series with Schur function argument; the theory of orthogonal polynomials and expansions, including generalizations of Szegö type asymptotics and connections with Jacobi matrices; the convergence theory for Padé and Hermite-Padé approximants, with emphasis on techniques from potential theory; material on wavelets and fractals and their relationship to invariant measures and nonlinear approximation; generalizations of de Brange's in equality for univalent functions in a quasi-orthogonal Hilbert space setting; applications of results concerning approximation by entire functions and the problem of analytic continuation; and other topics.

Author : Themistocles M. Rassias
Publisher : Springer
Page : 555 pages
File Size : 48,6 Mb
Release : 2014-11-18
Category : Mathematics
ISBN : 9781493912469

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Handbook of Functional Equations by Themistocles M. Rassias Pdf

As Richard Bellman has so elegantly stated at the Second International Conference on General Inequalities (Oberwolfach, 1978), “There are three reasons for the study of inequalities: practical, theoretical, and aesthetic.” On the aesthetic aspects, he said, “As has been pointed out, beauty is in the eye of the beholder. However, it is generally agreed that certain pieces of music, art, or mathematics are beautiful. There is an elegance to inequalities that makes them very attractive.” The content of the Handbook focuses mainly on both old and recent developments on approximate homomorphisms, on a relation between the Hardy–Hilbert and the Gabriel inequality, generalized Hardy–Hilbert type inequalities on multiple weighted Orlicz spaces, half-discrete Hilbert-type inequalities, on affine mappings, on contractive operators, on multiplicative Ostrowski and trapezoid inequalities, Ostrowski type inequalities for the Riemann–Stieltjes integral, means and related functional inequalities, Weighted Gini means, controlled additive relations, Szasz–Mirakyan operators, extremal problems in polynomials and entire functions, applications of functional equations to Dirichlet problem for doubly connected domains, nonlinear elliptic problems depending on parameters, on strongly convex functions, as well as applications to some new algorithms for solving general equilibrium problems, inequalities for the Fisher’s information measures, financial networks, mathematical models of mechanical fields in media with inclusions and holes.

Author : Mohammad Bagher Ghaemi,Nahid Gharakhanlu,Themistocles M. Rassias,Reza Saadati
Publisher : Springer Nature
Page : 287 pages
File Size : 43,6 Mb
Release : 2021-07-11
Category : Mathematics
ISBN : 9783030760472

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Advances in Matrix Inequalities by Mohammad Bagher Ghaemi,Nahid Gharakhanlu,Themistocles M. Rassias,Reza Saadati Pdf

This self-contained monograph unifies theorems, applications and problem solving techniques of matrix inequalities. In addition to the frequent use of methods from Functional Analysis, Operator Theory, Global Analysis, Linear Algebra, Approximations Theory, Difference and Functional Equations and more, the reader will also appreciate techniques of classical analysis and algebraic arguments, as well as combinatorial methods. Subjects such as operator Young inequalities, operator inequalities for positive linear maps, operator inequalities involving operator monotone functions, norm inequalities, inequalities for sector matrices are investigated thoroughly throughout this book which provides an account of a broad collection of classic and recent developments. Detailed proofs for all the main theorems and relevant technical lemmas are presented, therefore interested graduate and advanced undergraduate students will find the book particularly accessible. In addition to several areas of theoretical mathematics, Matrix Analysis is applicable to a broad spectrum of disciplines including operations research, mathematical physics, statistics, economics, and engineering disciplines. It is hoped that graduate students as well as researchers in mathematics, engineering, physics, economics and other interdisciplinary areas will find the combination of current and classical results and operator inequalities presented within this monograph particularly useful.