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On Solutions of Some Generalizations of the Goła̧b–Schinzel Equation

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Functional Equations in Mathematical Analysis

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

Abstract

This paper is a survey devoted to the functional equation

$$f(x + M(f(x))y) = f(x)f(y),$$

which ‘connects’ the Goła̧b–Schinzel equation with the exponential one, and to its generalization

$$f(x + M(f(x))y) = H(f(x),f(y)).$$

Our considerations refer to the paper :  Brzdȩk, J.: The Goła̧b–Schinzel equation and its generalizations. Aequationes Math. 70, 14–24 (2005)

Mathematics Subject Classification (2000): Primary 39B52

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Authors and Affiliations

  1. Department of Mathematics, Rzeszów University of Technology, W. Pola 2, 35–959, Rzeszów, Poland

    Eliza Jabłońska

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  1. Eliza Jabłońska
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Correspondence to Eliza Jabłońska .

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  1. , Department of Mathematics, National Technical University of Athens, Iroon Polytechneiou 9, Athens, 15780, Greece

    Themistocles M. Rassias

  2. Institute of Mathematics, Pedagogical University, ul. Podchorazych 2, Krakow, 30-084, Poland

    Janusz Brzdek

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Jabłońska, E. (2011). On Solutions of Some Generalizations of the Goła̧b–Schinzel Equation. In: Rassias, T., Brzdek, J. (eds) Functional Equations in Mathematical Analysis. Springer Optimization and Its Applications(), vol 52. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0055-4_32

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