Functional equations, inequalities, and applications

**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. Front Matter....Pages i-vii Hyers-Ulam Stability of a Quadratic Functional Equation in Banach Modules....Pages 1-10 Cauchy and Pexider Operators in Some Function Spaces....Pages 11-19 The Median Principle for Inequalities and Applications....Pages 21-37 On the Hyers-Ulam-Rassias Stability of a Pexiderized Quadratic Equation II....Pages 39-65 On the Hyers-Ulam-Rassias Stability of a Functional Equation....Pages 67-71 A Pair of Functional Inequalities of Iterative Type Related to a Cauchy Functional Equation....Pages 73-89 On Approximate Algebra Homomorphisms....Pages 91-104 Hadamard and Dragomir-Agarwal Inequalities, the Euler Formulae and Convex Functions....Pages 105-137 On Ulam Stability in the Geometry of PDE’s....Pages 139-147 On Certain Functional Equations and Mean Value Theorems....Pages 149-158 Some General Approximation Error and Convergence Rate Estimates in Statistical Learning Theory....Pages 159-165 Functional Equations on Hypergroups....Pages 167-181 The Generalized Cauchy Functional Equation....Pages 183-189 On the Aleksandrov-Rassias Problem for Isometric Mappings....Pages 191-221 Back Matter....Pages 223-224