Abstract
AbstractLet{(X,*)}be a hypergroup and let{w_{0}}be a fixed measure onX. In this paper we study the two functional equations\langle\delta_{x}*\delta_{y}*\omega_{0},g\rangle+\langle\delta_{x}*\delta_{% \check{y}}*\omega_{0},g\rangle=2g(x)g(y),\quad x,y\in X,and\langle\delta_{x}*\delta_{\check{y}}*\omega_{0},f\rangle-\langle\delta_{x}*% \delta_{y}*\omega_{0},f\rangle=2f(x)f(y),\quad x,y\in X,where{g,f:X\to\mathbb{C}}are continuous and bounded functions to be determined. We express the solutions of the two functional equations in terms of multiplicative maps on{(X,*)}. As an application we give the solution of the two functional equations on polynomial and Sturm–Liouville hypergroups.
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