Developments in Functional Equations and Related Topics

ISBN-13: 9783319617312 / Angielski / Twarda / 2017 / 352 str.

Janusz Brzdȩk; Krzysztof Ciepliński; Themistocles M. Rassias

Spis treści

1. The behavior of the difference between two means (Shoshana Abramovich).- 2. Isometric approximation in bounded sets and its applications (Pekka Alestalo).- 3.On the indicator plurality function (.25in; font-size: 10pt; line-height: 115%; font-family: NimbusRomNo9L-Regu;">Anna Bahyrycz).- 4.The translation equation in the ring of formal power series over C and formal functional equations (Harald Fripertinger and Ludwig Reich).- 5. Fischer-Muszély additivity – a half century story (Roman Ger).- 6.Alien functional equations – a selective survey of results (Roman Ger and Maciej Sablik).- 7.Remarks on analogies between Haar meager sets and Haar null sets (Eliza Jabłońska).- 8.On some inequalities inspired by the stability of dynamical system (Zenon Moszner).- 9. Homomorphisms from Functional Equations in Probability (Adam J. Ostaszewski).- 10.Recent developments in the translation equation and its stability (Barbara Przebieracz).- 11.On some recent applications of stochastic c

onvex ordering theorems to some functional inequalities for convex functions – a survey (Teresa Rajba).- 12.On the construction of the field of reals by means of functional equations and their stability and related topics (Jens Schwaiger).- 13.Generalized Dhombres functional equation (Jaroslav Smítal and Marta Štefánková).- 14.Functional equations and stability problems on hypergroups (László Székelyhidi).- 15.Stability of systems of general functional equations in the compact-open topology (Pavol Zlatoš).

Blurb

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.