Functional Equations -- Results and Advances / Edition 1

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The theory of functional equations has been developed in a rapid and productive way in the second half of the Twentieth Century. This is due to the fact that the mathematical applications increased the number of investigations of newer and newer types of functional equations. At the same time, the self-development of this theory was also very fruitful.
The material of this volume reflects very well the complexity and applicability of the most active research fields. The results and methods contained give a representative crossection of what is recently happening in the theory of functional equations.

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Product Details

  • ISBN-13: 9781402004858
  • Publisher: Springer US
  • Publication date: 2/28/2002
  • Series: Advances in Mathematics Series, #3
  • Edition description: 2002
  • Edition number: 1
  • Pages: 361
  • Product dimensions: 6.34 (w) x 9.86 (h) x 1.00 (d)

Table of Contents

Preface. Part I: Classical Functional Equations and Inequalities. On some trigonometric functional inequalities; R. Badora, R. Ger. On the continuity of additive-like functions and Jensen convex functions which are Borel on a sphere; K. Baron. Note on a functional-differential inequality; B. Choczewski. A characterization of stationary sets for the class of Jensen convex functions; R. Ger, K. Nikodem. On the characterization of Weierstrass's sigma function; A. Járai, W. Sander. On a Mikusinski-Jensen functional equation; K. Lajkó, Z. Páles. Part II: Stability of Functional Equations. Stability of the multiplicative Cauchy equation in ordered fields; Z. Boros. On approximately monomial functions; A. Gilányi. Les opérateurs de Hyers; Z. Moszner. Geometrical aspects of stability; J. Tabor, J. Tabor. Part III: Functional Equations in One Variable and Iteration Theory. On semi-conjugacy equation for homeomorphisms of the circle; K. Cieplinski, M. Cezary Zdun. A survey of results and open problems on the Schilling equation; R. Girgensohn. Properties of an operator acting on the space of bounded real functions and certain subspaces; H.-H. Kairies. Part IV: Composite Functional Equations and Theory of Means. A Matkowski-Sutô type problem for quasi-arithmetic means of order alpha; Z. Daróczy, Z. Páles. An extension theorem for conjugate arithmetic means; G. Hajdu. Homogeneous Cauchy mean values; L. Losonczi. On invariant generalized Beckenbach-Gini means; J. Matkowski. Final part of the answer to a Hilbert's question; M. Sablik. Part V: Functional Equations on Algebraic Structures. A generalization of d'Alembert'sfunctional equation; T.M.K. Davison. About a remarkable functional equation on some restricted domains; F. Skof. On discrete spectral synthesis; L. Székelyhidi. Hyers theorem and the cocycle property; J. Tabor. Part VI: Functional Equations in Functional Analysis. Mappings whose derivatives are isometries; J.A. Baker. Localizable functionals; B. Ebanks. Jordan maps on standard operator algebras; L. Molnár. Part VII: Bisymmetry and Associativity Type Equations on Quasigroups. On the functional equation S1(x, y) = S2(x, T(N(x),y)); C. Alsina, E. Trillas. Generalized associativity on rectangular quasigroups; A. Krapež. The aggregation equation: solutions with non intersecting partial functions; M. Taylor.

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