Hyers-Ulam-Rassias stability of functional equations in nonlinear analysis

✍ Scribed by Soon-Mo Jung (auth.)

• Publisher: Springer-Verlag New York
• Year: 2011
• Tongue: English
• Leaves: 377
• Series: Springer Optimization and Its Applications 48
• Edition: 1
• Category: Library

✦ Synopsis

This textbook at the advanced undergraduate/graduate level will complement the books of D.H. Hyers, G. Isac, and Th.M. Rassias (© Birkhauser 1998) and of S. Czerwik (2002) by integrating and presenting the primary developments applying to almost all the classical results of the Hyers-Ulam-Rassias stability.

The self-contained text is presented in an easy to understand fashion and all the necessary materials and information are included in order to appeal to a diverse audience with interests in difference and functional equations and functional analysis. Highlights of the text include discussions of the method of invariant means and the fixed point method, the stability problems for the exponential functional equations, Hyers-Ulam stability, Hyers-Ulam-Rassias stability, Pexider equation, and superstability of the exponential function.

✦ Table of Contents

Front Matter....Pages i-xiii
Introduction....Pages 1-17
Additive Cauchy Equation....Pages 19-86
Generalized Additive Cauchy Equations....Pages 87-103
Hosszú’s Functional Equation....Pages 105-122
Homogeneous Functional Equation....Pages 123-142
Linear Functional Equations....Pages 143-153
Jensen’s Functional Equation....Pages 155-174
Quadratic Functional Equations....Pages 175-205
Exponential Functional Equations....Pages 207-225
Multiplicative Functional Equations....Pages 227-251
Logarithmic Functional Equations....Pages 253-266
Trigonometric Functional Equations....Pages 267-284
Isometric Functional Equation....Pages 285-323
Miscellaneous....Pages 325-343
Back Matter....Pages 345-362

✦ Subjects

Difference and Functional Equations; Analysis; Functional Analysis