D’Alembert’s Functional Equation and Superstability Problem in Hypergroups

D. Zeglami (), A. Roukbi () and Themistocles M. Rassias ()
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D. Zeglami: E.N.S.A.M., Moulay Ismail University
A. Roukbi: Ibn Tofail University
Themistocles M. Rassias: National Technical University of Athens

A chapter in Handbook of Functional Equations, 2014, pp 367-396 from Springer

Abstract: Abstract Our main goal is to determine the continuous and bounded complex valued solutions of the functional equation $$ \langle \delta_{x}\ast \delta_{y},g\rangle +\langle \delta_{x}\ast \delta_{\check{y}},g\rangle =2~g(x)g(y),\;x,y\in X,$$ where X is a hypergroup. The solutions are expressed in terms of 2 -dimensional representations of X. The papers of Davison [10] and Stetkaer [25, 26] are the essential motivation for this first part of the present work and the methods used here are closely related to and inspired by those in [10, 25, 26]. In addition, superstability problem for this functional equation on any hypergroup and without any condition on f is considered.

Keywords: Superstability; Hypergroup; D’ Alembert’s functional equation; Involution; Wilson’s functional equation (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4939-1286-5_17

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DOI: 10.1007/978-1-4939-1286-5_17

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