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Functional Equations in Mathematical Analysis

  • Book
  • © 2012

Overview

Editors:
  1. Themistocles M. Rassias

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

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    You can also search for this editor in PubMed   Google Scholar

  2. Janusz Brzdek

    1. Institute of Mathematics, Pedagogical University, Krakow, Poland

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  • Presents the most recent results to the solution of the Ulam stability problem for several types of functional equations
  • Includes contributions from an international group of experts in the fields of functional analysis, partial differential equations, dynamical systems, algebra, geometry, and physics
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Optimization and Its Applications (SOIA, volume 52)

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Table of contents (48 chapters)

  1. Front Matter

    Pages i-xvii
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  2. Stability in Mathematical Analysis

    1. Front Matter

      Pages 1-1
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    2. Stability Properties of Some Functional Equations

      • Roman Badora
      Pages 3-13

    3. Note on Superstability of Mikusiński’s Functional Equation

      • Bogdan Batko
      Pages 15-17

    4. A General Fixed Point Method for the Stability of Cauchy Functional Equation

      • Liviu Cădariu, Viorel Radu
      Pages 19-32

    5. Orthogonality Preserving Property and its Ulam Stability

      • Jacek ChmieliÅ„ski
      Pages 33-58

    6. On the Hyers–Ulam Stability of Functional Equations with Respect to Bounded Distributions

      • Jae-Young Chung
      Pages 59-78

    7. Stability of Multi-Jensen Mappings in Non-Archimedean Normed Spaces

      • Krzysztof CiepliÅ„ski
      Pages 79-86

    8. On Stability of the Equation of Homogeneous Functions on Topological Spaces

      • Stefan Czerwik
      Pages 87-96

    9. Hyers–Ulam Stability of the Quadratic Functional Equation

      • Elhoucien Elqorachi, Youssef Manar, Themistocles M. Rassias
      Pages 97-105

    10. Intuitionistic Fuzzy Approximately Additive Mappings

      • M. Eshaghi-Gordji, H. Khodaei, H. Baghani, M. Ramezani
      Pages 107-124

    11. Generalized Hyers–Ulam Stability for General Quadratic Functional Equation in Quasi-Banach Spaces

      • Jinmei Gao
      Pages 125-138

    12. Ulam Stability Problem for Frames

      • Laura GăvruÅ£a, PaÅŸc GăvruÅ£a
      Pages 139-152

    13. Generalized Hyers–Ulam Stability of a Quadratic Functional Equation

      • Kil-Woung Jun, Hark-Mahn Kim, Jiae Son
      Pages 153-164

    14. On the Hyers–Ulam–Rassias Stability of the Bi-Pexider Functional Equation

      • Kil-Woung Jun, Yang-Hi Lee
      Pages 165-175

    15. Approximately Midconvex Functions

      • Krzysztof Misztal, Jacek Tabor, Józef Tabor
      Pages 177-190

    16. The Hyers–Ulam and Ger Type Stabilities of the First Order Linear Differential Equations

      • Takeshi Miura, Go Hirasawa
      Pages 191-199

    17. On the Butler–Rassias Functional Equation and its Generalized Hyers–Ulam Stability

      • Takeshi Miura, Go Hirasawa, Takahiro Hayata
      Pages 201-206

    18. A Note on the Stability of an Integral Equation

      • Takeshi Miura, Go Hirasawa, Sin-Ei Takahasi, Takahiro Hayata
      Pages 207-222

    19. On the Stability of Polynomial Equations

      • Abbas Najati, Themistocles M. Rassias
      Pages 223-227
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Keywords

About this book

The stability problem for approximate homomorphisms, or the Ulam stability problem, was posed by S. M. Ulam in the year 1941. The solution of this problem for various classes of equations is an expanding area of research. In particular, the pursuit of solutions to the Hyers-Ulam and Hyers-Ulam-Rassias stability problems for sets of functional equations and ineqalities has led to an outpouring of recent research.

 

This volume, dedicated to S. M. Ulam, presents the most recent results on the solution to Ulam stability problems for various classes of functional equations and inequalities. Comprised of invited contributions from notable researchers and experts, this volume presents several important types of functional equations and inequalities and their applications to problems in mathematical analysis, geometry, physics and applied mathematics.

 

"Functional Equations in Mathematical Analysis" is intended for researchers and students in mathematics, physics, and other computational and applied sciences.

Editors and Affiliations

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

    Themistocles M. Rassias

  • Institute of Mathematics, Pedagogical University, Krakow, Poland

    Janusz Brzdek

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