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Functional Equations — Results and Advances

  • Book
  • © 2002

Overview

Editors:
  1. Zoltán Daróczy

    1. Institute of Mathematics and Informatics, University of Debrecen, Hungary

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  2. Zsolt Páles

    1. Institute of Mathematics and Informatics, University of Debrecen, Hungary

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Advances in Mathematics (ADMA, volume 3)

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Table of contents (28 chapters)

  1. Front Matter

    Pages i-x
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  2. Classical Functional Equations and Inequalities

    1. Front Matter

      Pages 1-1
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    2. On Some Trigonometric Functional Inequalities

      • Roman Badora, Roman Ger
      Pages 3-15

    3. On the Continuity of Additive—Like Functions and Jensen Convex Functions which are Borel on a Sphere

      • Karol Baron
      Pages 17-20

    4. Note on a Functional—Differential Inequality

      • Bogdan Choczewski
      Pages 21-24

    5. A Characterization of Stationary Sets for the Class of Jensen Convex Functions

      • Roman Ger, Kazimierz Nikodem
      Pages 25-28

    6. On the Characterization of Weierstrass’s Sigma Function

      • Antal Járai, Wolfgang Sander
      Pages 29-79

    7. On a Mikusiński—Jensen Functional Equation

      • Károly Lajkó, Zsolt Páles
      Pages 81-87

  3. Stability of Functional Equations

    1. Front Matter

      Pages 89-89
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    2. Stability of the Multiplicative Cauchy Functional Equation in Ordered Fields

      • Zoltán Boros
      Pages 91-98

    3. On Approximately Monomial Functions

      • Attila Gilányi
      Pages 99-111

    4. Les Opérateurs de Hyers

      • Zenon Moszner
      Pages 113-122

    5. Geometrical Aspects of Stability

      • Jacek Tabor, Józef Tabor
      Pages 123-132

  4. Functional Equations in One Variable and Iteration Theory

    1. Front Matter

      Pages 133-133
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    2. On Semi-Conjugacy Equation for Homeomorphisms of the Circle

      • Krzysztof Ciepliński, Marek Cezary Zdun
      Pages 135-158

    3. A Survey of Results and Open Problems on the Schilling Equation

      • Roland Girgensohn
      Pages 159-174

    4. Properties of an Operator Acting on the Space of Bounded Real Functions and Certain Subspaces

      • Hans-Heinrich Kairies
      Pages 175-186

  5. Composite Functional Equations and Theory of Means

    1. Front Matter

      Pages 187-187
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    2. A Matkowski-Sutô Type Problem for Quasi-Arithmetic Means of Order α

      • Zoltán Daróczy, Zsolt Páles
      Pages 189-200

    3. An Extension Theorem for the Matkowski—Sutô Problem for Conjugate Arithmetic Means

      • Gabriella Hajdu
      Pages 201-208
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Keywords

About this book

The theory of functional equations has been developed in a rapid and productive way in the second half of the Twentieth Century. First of all, this is due to the fact that the mathematical applications raised the investigations of newer and newer types of functional equations. At the same time, the self development of this theory was also very fruitful. This can be followed in many monographs that treat and discuss the various methods and approaches. These developments were also essentially influenced by a number jour­ nals, for instance, by the Publicationes Mathematicae Debrecen (founded in 1953) and by the Aequationes Mathematicae (founded in 1968), be­ cause these journals published papers from the field of functional equa­ tions readily and frequently. The latter journal also publishes the yearly report of the International Symposia on Functional Equations and a comprehensive bibliography of the most recent papers. At the same time, there are periodically and traditionally organized conferences in Poland and in Hungary devoted to functional equations and inequali­ ties. In 2000, the 38th International Symposium on Functional Equations was organized by the Institute of Mathematics and Informatics of the University of Debrecen in Noszvaj, Hungary. The report about this meeting can be found in Aequationes Math. 61 (2001), 281-320.

Editors and Affiliations

  • Institute of Mathematics and Informatics, University of Debrecen, Hungary

    Zoltán Daróczy, Zsolt Páles

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