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Developments in functional equations and related topics

Author: Janusz Brzdȩk
Publisher: Cham : Springer, ©2017.
Series: Springer optimization and its applications, v. 124.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book presents current research on Ulam stability for functional equations and inequalities. Contributions from renowned scientists emphasize fundamental and new results, methods and techniques. Detailed examples are given to theories to further understanding at the graduate level for students in mathematics, physics, and engineering. Key topics covered in this book include: Quasi means Approximate isometries  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Developments in functional equations and related topics.
Cham : Springer, ©2017
(OCoLC)988282577
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Janusz Brzdȩk
ISBN: 9783319617329 331961732X
OCLC Number: 1001336124
Description: 1 online resource
Contents: Preface; Contents; List of Contributors; 1 The Behavior of the Difference Between Two Means; 1.1 Introduction; 1.2 The Behavior of Mp(x1,x2) -Wq(x1,x2); 1.3 Inequalities for Quasi-Arithmetic Means and Subquadracity; References; 2 Isometric Approximation in Bounded Sets and Its Applications; 2.1 Introduction; 2.2 Isometric Approximation in Bounded Sets; 2.3 From Approximation to Bilipschitz Extension; 2.4 From Approximation to Quasisymmetric Extension; References; 3 On the Indicator Plurality Function; 3.1 Introduction; 3.2 The Plurality Function and the Indicator Plurality Function. 3.3 On the Functions Which Are Consistent3.4 Construction of All m-Elements Consistent System; 3.5 On the Multifunctions Related to the Plurality Function; References; 4 The Translation Equation in the Ring of Formal Power Series Over C and Formal Functional Equations; 4.1 Introduction; 4.1.1 The Embedding Problem; 4.1.2 The Ring of Formal Power Series with Complex Coefficients; 4.1.3 Iteration Groups; 4.1.4 The Main Problems; 4.2 First Classification of Iteration Groups; 4.2.1 Systems of Functional Equations for the Coefficient Functions; 4.2.2 Formal Functional Equations. 4.2.3 Differential Equations Obtained from the Translation Equation4.2.4 The Relevance of Aczél-Jabotinsky Differential Equations; 4.2.5 Reordering the Summands; 4.3 Solving the Translation Equation by a Purely Algebraic Differentiation Process; 4.3.1 Formal Iteration Groups of Type I Obtained from (PDform, I) and (B, I); 4.3.2 Formal Iteration Groups of Type I Obtained from (Dform, I) and (B, I); 4.3.3 Formal Iteration Groups of Type I Obtained from (AJform, I) and (B, I); 4.3.4 Normal Forms of Iteration Groups of Type I. 4.3.5 Formal Iteration Groups of Type (II, k) Obtained from the Three Differential Equations4.3.6 Normal Forms of Iteration Groups of Type (II, k) ; 4.4 Concluding Remarks and Open Problems; References; 5 Fischer-Muszély Additivity: A Half Century Story; 5.1 Background; 5.2 Fischer-Muszély Equation; 5.3 General Solution; 5.3.1 Preliminary Results; 5.3.2 Main Result; 5.3.3 Derivation of Earlier Results; 5.4 The Hierarchy of (Non)Commutativity; 5.5 Pexiderization; 5.5.1 Solutions Admitting Zeros; 5.5.2 Basic Equation and Additivity; 5.5.3 Solutions with Values in Inner Product Spaces. 5.6 Inequality Case5.7 Stability; References; 6 Alien Functional Equations: A Selective Survey of Results; 6.1 Introduction; 6.2 Extension of Dhombres's Results; 6.2.1 Even Solutions; 6.2.2 A Generalized Ring Homomorphisms Equation; 6.2.3 The Alienation of Additivity and Exponentiality; 6.2.3.1 Some Lemmas; 6.2.3.2 Main Results; 6.2.3.3 Quadratic Equivalence and the Crucial Result; 6.2.4 Alienation of Additive and Logarithmic Equations; 6.3 Functional Equations Stemming from Actuarial Mathematics; 6.3.1 Positive Results on Alienation of Hosszú and Other Cauchy Equations.
Series Title: Springer optimization and its applications, v. 124.
Responsibility: Janusz Brzdȩk [and others], editors.

Abstract:

This book presents current research on Ulam stability for functional equations and inequalities. Contributions from renowned scientists emphasize fundamental and new results, methods and techniques. Detailed examples are given to theories to further understanding at the graduate level for students in mathematics, physics, and engineering. Key topics covered in this book include: Quasi means Approximate isometries Functional equations in hypergroups Stability of functional equations Fischer-Muszély equation Haar meager sets and Haar null sets Dynamical systems Functional equations in probability theory Stochastic convex ordering Dhombres functional equation Nonstandard analysis and Ulam stability This book is dedicated in memory of Staniłsaw Marcin Ulam, who posed the fundamental problem concerning approximate homomorphisms of groups in 1940; which has provided the stimulus for studies in the stability of functional equations and inequalities.

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