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

In: Functional Equations in Mathematical Analysis

Author

Listed:
  • D. Zeglami

    (Ibn Tofail University)

  • S. Kabbaj

    (Ibn Tofail University)

  • A. Charifi

    (Ibn Tofail University)

  • A. Roukbi

    (Ibn Tofail University)

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.

Suggested Citation

  • D. Zeglami & S. Kabbaj & A. Charifi & A. Roukbi, 2011. "μ-Trigonometric Functional Equations and Hyers–Ulam Stability Problem in Hypergroups," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Janusz Brzdek (ed.), Functional Equations in Mathematical Analysis, chapter 0, pages 337-358, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-0055-4_26
    DOI: 10.1007/978-1-4614-0055-4_26
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