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Developments in Functional Equations and Related Topics

  • Book
  • Aug 2017

Overview

Editors:
  1. Janusz Brzdęk

    1. Department of Mathematics, Pedagogical University of Cracow, Kraków,, Poland

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  2. Krzysztof Ciepliński

    1. Faculty of Applied Mathematics, AGH University of Science and Technology, Kraków, Poland

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    You can also search for this editor in PubMed   Google Scholar

  3. Themistocles M. Rassias

    1. Department of Mathematics, National Technical University of Athens, Athens, Greece

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  • 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
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xii
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  2. The Behavior of the Difference Between Two Means

    • Shoshana Abramovich
    Pages 1-15

  3. Isometric Approximation in Bounded Sets and Its Applications

    • Pekka Alestalo
    Pages 17-24

  4. On the Indicator Plurality Function

    • Anna Bahyrycz
    Pages 25-40

  5. The Translation Equation in the Ring of Formal Power Series Over ℂ and Formal Functional Equations

    • Harald Fripertinger, Ludwig Reich
    Pages 41-69

  6. Fischer–Muszély Additivity: A Half Century Story

    • Roman Ger
    Pages 71-106

  7. Alien Functional Equations: A Selective Survey of Results

    • Roman Ger, Maciej Sablik
    Pages 107-147

  8. Remarks on Analogies Between Haar Meager Sets and Haar Null Sets

    • Eliza Jabłońska
    Pages 149-159

  9. On Some Inequalities Inspired by the Stability of Dynamical System

    • Zenon Moszner
    Pages 161-170

  10. Homomorphisms from Functional Equations in Probability

    • Adam J. Ostaszewski
    Pages 171-213

  11. Recent Developments in the Translation Equation and Its Stability

    • Barbara Przebieracz
    Pages 215-229

  12. On Some Recent Applications of Stochastic Convex Ordering Theorems to Some Functional Inequalities for Convex Functions: A Survey

    • Teresa Rajba
    Pages 231-274

  13. On the Construction of the Field of Reals by Means of Functional Equations and Their Stability and Related Topics

    • Jens Schwaiger
    Pages 275-295

  14. Generalized Dhombres Functional Equation

    • Jaroslav Smítal, Marta Štefánková
    Pages 297-303

  15. Functional Equations and Stability Problems on Hypergroups

    • László Székelyhidi
    Pages 305-331

  16. Stability of Systems of General Functional Equations in the Compact-Open Topology

    • Pavol Zlatoš
    Pages 333-352
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Keywords

About this book

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.

Editors and Affiliations

  • Department of Mathematics, Pedagogical University of Cracow, Kraków,, Poland

    Janusz Brzdęk

  • Faculty of Applied Mathematics, AGH University of Science and Technology, Kraków, Poland

    Krzysztof Ciepliński

  • Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

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