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© 2017

Developments in Functional Equations and Related Topics

  • Janusz Brzdęk
  • Krzysztof Ciepliński
  • Themistocles M. Rassias

Benefits

  • Unique reference for functional equations, inequalities, and Ulam’s type stability

  • Presents current developments in select topics in functional equations and inequalities

  • Maximizes reader insights into a variety of methods and techniques and provides detailed examples to further graduate level accessibility

Book

Part of the Springer Optimization and Its Applications book series (SOIA, volume 124)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Shoshana Abramovich
    Pages 1-15
  3. Anna Bahyrycz
    Pages 25-40
  4. Roman Ger, Maciej Sablik
    Pages 107-147
  5. Adam J. Ostaszewski
    Pages 171-213
  6. Jaroslav Smítal, Marta Štefánková
    Pages 297-303

About this book

Introduction

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.

Keywords

set-valued functional equations K-metric spaces Perov type fixed point theorems Haar meager sets linear functional equations inequalities in a single variable Ulam’s stability of linear operators stability of nearisometries Isometric approximation indicator plurality function ring of formal power series Fischer-Muszély additivity dynamical system Haar null sets Homomorphisms from Functional Equations stochastic convex ordering theorems Dhombres functional equation stability problems on hypergroups compact-open topology Stability of systems

Editors and affiliations

  • Janusz Brzdęk
    • 1
  • Krzysztof Ciepliński
    • 2
  • Themistocles M. Rassias
    • 3
  1. 1.Department of MathematicsPedagogical University of CracowKraków,Poland
  2. 2.Faculty of Applied MathematicsAGH University of Science and TechnologyKrakówPoland
  3. 3.Department of MathematicsNational Technical University of AthensAthensGreece

Bibliographic information