Functional Equations, Inequalities and Applications

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Themistocles M. Rassias
Springer Science & Business Media, Sep 30, 2003 - Mathematics - 224 pages

Functional Equations, Inequalities and Applications provides an extensive study of several important equations and inequalities, useful in a number of problems in mathematical analysis. Subjects dealt with include the generalized Cauchy functional equation, the Ulam stability theory in the geometry of partial differential equations, stability of a quadratic functional equation in Banach modules, functional equations and mean value theorems, isometric mappings, functional inequalities of iterative type, related to a Cauchy functional equation, the median principle for inequalities and applications, Hadamard and Dragomir-Agarwal inequalities, the Euler formulae and convex functions and approximate algebra homomorphisms. Also included are applications to some problems of pure and applied mathematics.

This book will be of particular interest to mathematicians and graduate students whose work involves functional equations, inequalities and applications.

 

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Contents

HYERSULAM STABILITY OF A QUADRATIC FUNCTIONAL EQUATION IN BANACH MODULES
1
CAUCHY AND PEXIDER OPERATORS IN SOME FUNCTION SPACES
11
THE MEDIAN PRINCIPLE FOR INEQUALITIES AND APPLICATIONS
21
ON THE HYERSULAMRASSIAS STABILITY OF A PEXIDERIZED QUADRATIC EQUATION II
39
ON THE HYERSULAMRASSIAS STABILITY OF A FUNCTIONAL EQUATION
67
A PAIR OF FUNCTIONAL INEQUALITIES OF ITERATIVE TYPE RELATED TO A CAUCHY FUNCTIONAL EQUATION
73
ON APPROXIMATE ALGEBRA HOMOMORPHISMS
91
HADAMARD AND DRAGOMIRAGARWAL INEQUALITIES THE EULER FORMULAE AND CONVEX FUNCTIONS
105
ON ULAM STABILITY IN THE GEOMETRY OF PDES
139
ON CERTAIN FUNCTIONAL EQUATIONS AND MEAN VALUE THEOREMS
149
SOME GENERAL APPROXIMATION ERROR AND CONVERGENCE RATE ESTIMATES IN STATISTICAL LEARNING THEORY
159
FUNCTIONAL EQUATIONS ON HYPERGROUPS
167
THE GENERALIZED CAUCHY FUNCTIONAL EQUATION
183
ON THE ALEKSANDROVRASSIAS PROBLEM FOR ISOMETRIC MAPPINGS
191
Index
223
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