Bouikhalene, Belaid; Elqorachi, Elhoucien On Stetkær type functional equations and Hiers-Ulam stability. (English) Zbl 1111.39021 Publ. Math. Debr. 69, No. 1-2, 95-120 (2006). Given a locally compact group \(G\), a compact subgroup \(K\) of the group of morphisms of \(G\), a character \(\chi:K\to\mathbb C\), and a \(K\)-invariant bounded measure on \(G\), the authors investigate the functional equation \[ \int_G\int_K f(xtk\cdot y)\overline{\chi}(k)dkd\mu(t)=g(x)h(y), \qquad x,y\in G, \tag{(1)} \] where \(f,g,h\in C_b(G)\) are unknown functions. This equation contains, as a particular case, the D’Alembert and Wilson functional equations.The main results of the paper describe the connection of the solutions equation (1) to the solutions of Badora’s functional equation \[ \int_G\int_K f(xtk\cdot y)dkd\mu(t)=f(x)f(y), \qquad x,y\in G. \] The Hyers-Ulam stability problem of equation (1) is also studied, and a superstability-type result is obtained. Reviewer: Zsolt Páles (Debrecen) Cited in 1 ReviewCited in 1 Document MSC: 39B52 Functional equations for functions with more general domains and/or ranges 39B82 Stability, separation, extension, and related topics for functional equations 22D05 General properties and structure of locally compact groups Keywords:functional equation; Gelfand measure; spherical function; Hyers-Ulam stability; locally compact group; Wilson functional equations; Badora’s functional equation; D’Alembert functional equation; Stetkaer functional equation PDFBibTeX XMLCite \textit{B. Bouikhalene} and \textit{E. Elqorachi}, Publ. Math. Debr. 69, No. 1--2, 95--120 (2006; Zbl 1111.39021)