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.
Reihe
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Produkt-Hinweis
Maße
Höhe: 254 mm
Breite: 172 mm
Dicke: 33 mm
Gewicht
ISBN-13
978-981-4317-62-7 (9789814317627)
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Schweitzer Klassifikation
Autor*in
The University Of Memphis, Usa
Advanced Univariate Ostrowski Type Inequalities; Higher Order Ostrowski Inequalities; Multidimensional Euler Identity and Optimal Multidimensional Ostrowski Inequalities; More on Multidimensional Ostrowski Type Inequalities; Ostrowski Inequalities on Euclidean Domains; High Order Ostrowski Inequalities on Euclidean Domains; Ostrowski Inequalities on Spherical Shells; Ostrowski Inequalities on Balls and Shells Via Taylor-Widder Formula; Multivariate Opial Type Inequalities for Functions Vanishing at an Interior Point; General Multivariate Weighted Opial Inequalities; Opial Inequalities for Widder Derivatives; and other papers.