Frontiers in Functional Equations and Analytic Inequalities

ISBN-13: 9783030289492 / Angielski / Twarda / 2019 / 753 str.

George Anastassiou; John Michael Rassias

Spis treści

TOC: TABLE OF CONTENTS:

1.       Functional Equations and Applications

2.       Methods of Solving Functional Equations

3.       General Solution of Euler–Lagrange  Type Functional Equations

4.      General Solution of Euler–Lagrange-Jensen Type Functional Equations

5.       General Solution of Cubic , Quartic Type Functional Equations

6.       Solution of Quintic , Sextic, Septic, Octic,…, Functional Equations

7.      Mixed Type Functional Equations   

8.      Two-Variable and Functional Equations in Several Variables

9.       The Famous Ulam Stability Problem

10.  Ulam Stability of Functional Equations in Various Spaces

11.  Approximation and Functional Inequalities

12.   Ulam–Hyers Stabilities of Functional Equations in  Normed Spaces

13.   Stabilities of Functional Equations on C*-algebras and Lie C*-algebras

14.   Ulam Stability of Mixed Type Mappings on Restricted Domains

15.  Related Topics on Distributions and Hyperfunctions

16.  Ostrowski inequalities

17.  Opial inequalities

18.  Poincare inequalities

19.  Sobolev inequalities

20.  Polya inequalities

21.  Means inequalities

22.  Gruss inequalities

23.  Fractional differentiation inequalities

24.  Operator inequalities

25.  Multivariate domain inequalities on cube and sphere

26.  Time scale inequalities and fractionality

27.  Stochastic inequalities

28.  Csiszar f-divergence representations and estimates

29.  Inequalities of Hermite-Hadamard type

30.  Inequalities for Convex Functions

O autorze

George Anastassiou is Professor at the University of Memphis. Research interests include Computational analysis, approximation theory, probability, theory of moments. Professor Anastassiou has authored and edited several publications with Springer including "Fractional Differentiation Inequalities" (c) 2009, "Fuzzy Mathematics: Approximation Theory" (c) 2010, "Intelligent Systems: Approximation by Artificial Neural Networks" (c) 2014, "The History of Approximation Theory" (c) 2005, "Modern Differential Geometry in Gauge Theories" (c) 2006, and more.

John Michael Rassias is a Ph.D. graduate of the University of California, Berkeley. He is currently  Emeritus Professor of the National and Kapodistrian University of Athens, Greece. Professor John M. Rassias  is a leading mathematician and researcher in Mathematics. He has published academic papers in the following research areas: Functional Equations and Inequalities (more than 300 papers) in peer-reviewed leading scientific journals. Partial Differential Equations (more than 100 papers). He has also published 36  books and monographs in  Mathematics.

Blurb

This volume presents cutting edge research from the frontiers of functional equations and analytic inequalities active fields. It covers the subject of functional equations in a broad sense, including but not limited to the following topics: 

• Hyperstability of a linear functional equation on restricted domains
• Hyers–Ulam’s stability results to a three point boundary value problem of nonlinear fractional order differential equations
• Topological degree theory and Ulam’s stability analysis of a boundary value problem of fractional differential equations
• General Solution and Hyers-Ulam Stability of Duo Trigintic Functional Equation in Multi-Banach Spaces
• Stabilities of Functional Equations via Fixed Point Technique
• Measure zero stability problem for the Drygas functional equation with complex involution
• Fourier Transforms and Ulam Stabilities of Linear Differential Equations
• Hyers–Ulam stability of a discrete diamond–alpha derivative equation
• Approximate solutions of an interesting new mixed type additive-quadratic-quartic functional equation. 
  

The diverse selection of inequalities covered includes Opial, Hilbert-Pachpatte, Ostrowski, comparison of means, Poincare, Sobolev, Landau, Polya-Ostrowski, Hardy, Hermite-Hadamard, Levinson, and complex Korovkin type. The inequalities are also in the environments of Fractional Calculus and Conformable Fractional Calculus. Applications from this book's results can be found in many areas of pure and applied mathematics, especially in ordinary and partial differential equations and fractional differential equations. As such, this volume is suitable for researchers, graduate students and related seminars, and all science and engineering libraries. The exhibited thirty six chapters are self-contained and can be read independently and interesting advanced seminars can be given out of this book.