Handbook of functional equations Stability theory / Themistocles M. Rassias, ed.
Preface; Contents; Contributors; On Some Functional Equations; 1.1 Introduction; 1.2 The Decomposition Method; 1.3 Convergence Result; 2.1 The Collocation Method; 2.2 The Method of Moments; 2.3 The Least Squares Method; 2.4 The Adomian Decomposition Method; 3.1 Introduction; 3.2 Stability; Reference...
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
New York, NY u.a.
Springer
2014
|
| Schriftenreihe: | Springer optimization and its applications
96 |
| Schlagworte: | |
| Online Zugang: | Inhaltsverzeichnis Inhaltstext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Tag hinzufügen | Zusammenfassung: | Preface; Contents; Contributors; On Some Functional Equations; 1.1 Introduction; 1.2 The Decomposition Method; 1.3 Convergence Result; 2.1 The Collocation Method; 2.2 The Method of Moments; 2.3 The Least Squares Method; 2.4 The Adomian Decomposition Method; 3.1 Introduction; 3.2 Stability; References; 1 On the Convergence of Adomian's Method; Remarks on Stability of the Equation of Homomorphism for Square Symmetric Groupoids; 1 Introduction; 2 Approximation Methods for Solving Functional Equations; 2 An Auxiliary Result 3 Stability of the Generalized Quadratic Functional Equation on Topological Spaces3 Modified Stability on Square Symmetric Groupoids; 4 Some Complementary Results; References; On Stability of the Linear and Polynomial Functional Equations in Single Variable; 1 Introduction; 2 Stability of Zeros of Polynomials; 3 Stability of the Linear Equation: The General Case; 4 Stability of the Linear Equation: Iterative Case; 5 Set-Valued Case; 6 Stability of the Polynomial Equation; References; Selections of Set-valued Maps Satisfying Some Inclusions and the Hyers-Ulam Stability; 1 Introduction 2 Linear Inclusions3 Inclusions in a Single Variable; 4 Applications; References; Generalized Ulam-Hyers Stability Results: A Fixed Point Approach; 1 Preliminaries; 2 Results; References; On a Weak Version of Hyers-Ulam Stability Theorem in Restricted Domains; 1 Introduction; 2 A Weak Stability of Pexider Equation; 3 Weak Stability of Pexider Equation in Restricted Domains; References; On the Stability of Drygas Functional Equation on Amenable Semigroups; 1 Introduction; 2 Hyers-Ulam Stability of the Drygas Functional Equation in Amenable Semigroups; References Stability of Quadratic and Drygas Functional Equations, with an Application for Solving an Alternative Quadratic Equation1 Introduction; 2 Stability of the Quadratic Equation; 3 Stability of the Drygas Equation; 4 Alternative Quadratic Equation; References; A Functional Equation Having Monomials and Its Stability; 1 Introduction; 2 Preliminaries; 3 Multi-additive and Monomial Mappings; 4 Fixed Points and Stability of Monomial Functional Equations; References; Some Functional Equations Related to the Characterizations of Information Measures and Their Stability 1 Introduction and Preliminaries1.1 Information Measures; 1.2 The Characterization Problem and Functional Equations; 1.3 Prerequisites from the Theory of Functional Equations; 2 Results on the Fundamental Equation of Information and on the Sum Form Equations; 2.1 Information Functions; 2.2 Sum Form Equations; 3 Stability Problems; 3.1 The Cases α = 0 and 0 < α = 1; 3.2 The Case α < 0; 3.3 Related Equations; 3.3.1 Stability of the Entropy Equation; 3.3.2 Stability of the Modified Entropy Equation; 3.4 Stability of Sum Form Equations; References Approximate Cauchy-Jensen Type Mappings in Quasi-β-Normed Spaces This handbook consists of seventeen chapters written by eminent scientists from the international mathematical community, who present important research works in the field of mathematical analysis and related subjects, particularly in the Ulam stability theory of functional equations. The book provides an insight into a large domain of research with emphasis to the discussion of several theories, methods and problems in approximation theory, analytic inequalities, functional analysis, computational algebra and applications.The notion of stability of functional equations has its origins with S. M. Ulam, who posed the fundamental problem for approximate homomorphisms in 1940 and with D. H. Hyers, Th. M. Rassias, who provided the first significant solutions for additive and linear mappings in 1941 and 1978, respectively. During the last decade the notion of stability of functional equations has evolved into a very active domain of mathematical research with several applications of interdisciplinary nature.The chapters of this handbook focus mainly on both old and recent developments on the equation of homomorphism for square symmetric groupoids, the linear and polynomial functional equations in a single variable, the Drygas functional equation on amenable semigroups, monomial functional equation, the Cauchy-Jensen type mappings, differential equations and differential operators, operational equations and inclusions, generalized module left higher derivations, selections of set-valued mappings, D'Alembert's functional equation, characterizations of information measures, functional equations in restricted domains, as well as generalized functional stability and fixed point theory. |
|---|---|
| Beschreibung: | Literaturangaben |
| Beschreibung: | X, 396 S. |
| ISBN: | 9781493912858 978-1-4939-1285-8 |