μ-Trigonometric Functional Equations and Hyers–Ulam Stability Problem in Hypergroups

D. Zeglami (), S. Kabbaj (), A. Charifi () and A. Roukbi ()
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D. Zeglami: Ibn Tofail University
S. Kabbaj: Ibn Tofail University
A. Charifi: Ibn Tofail University
A. Roukbi: Ibn Tofail University

Chapter Chapter 26 in Functional Equations in Mathematical Analysis, 2011, pp 337-358 from Springer

Abstract: Abstract Let (X, ∗ ) be a hypergroup and μ be a complex bounded measure on X. We determine the continuous and bounded solutions of each of the following three functional equations $$\begin{array}{rcl} \left \langle {\delta }_{x} {_\ast} \mu {_\ast} {\delta }_{y},f\right \rangle & =& f(x)g(y) \pm g(x)f(y),\;x,y \in X, \\ \left \langle {\delta }_{x} {_\ast} \mu {_\ast} {\delta }_{y},g\right \rangle & =& g(x)g(y) + f(x)f(y),\;x,y \in X.\end{array}$$ In addition, when μ = δ e , Hyers–Ulam stability problems for these functional equations on hypergroups are considered. The results obtained in this paper are natural extensions of previous works done in groups especially by Stetkær, Elqorachi, Redouani, and Székelyhidi.

Keywords: Hypergroup; Trigonometric functionl equation; Hyers–Ulam stability; Spherical function; Polynomial hypergroup (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-1-4614-0055-4_26

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