Details

Autor(en) / Beteiligte

• Zeglami, D.
• Roukbi, A.
• Rassias, Themistocles M.

Titel

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

Ist Teil von

• Handbook of Functional Equations, 2014, Vol.96, p.367-396

Ort / Verlag

United States: Springer

Erscheinungsjahr

2014

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• Our main goal is to determine the continuous and bounded complex valued solutions of the functional equation\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$ \langle \delta_{x}\ast \delta_{y},g\rangle +\langle \delta_{x}\ast \delta_{\check{y}},g\rangle =2~g(x)g(y),\;x,y\in X,$$ \end{document} 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.