caa a22 4500 605508526 CHVBK 20210128100637.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s00010-014-0262-x doi (NATIONALLICENCE)springer-10.1007/s00010-014-0262-x Stability of Wilson's functional equations with involutions [Elektronische Daten] [Jaeyoung Chung, Prasanna Sahoo] Let S be a commutative semigroup, $${\mathbb{C}}$$ C the set of complex numbers, $${\mathbb{R}^+}$$ R + the set of nonnegative real numbers, $${f, g : S \to \mathbb{C}\, \, {\rm and} \, \, \sigma : S \to S}$$ f , g : S → C and σ : S → S an involution. In this article, we consider the stability of the Wilson's functional equations with involution, namely $${f(x + y) + f(x + \sigma y) = 2f(x)g(y)}$$ f ( x + y ) + f ( x + σ y ) = 2 f ( x ) g ( y ) and $${f(x + y) + f(x + \sigma y) = 2g(x)f(y)}$$ f ( x + y ) + f ( x + σ y ) = 2 g ( x ) f ( y ) for all $${x, y \in S}$$ x , y ∈ S in the spirit of Badora and Ger (Functional equations—results and advances, pp 3-15, 2002). As consequences of our results, we obtain the superstability of functional equations studied by Chung etal. (J Math Anal Appl 138:208-292, 1989), Chavez and Sahoo (Appl Math Lett 24:344-347, 2011) and Houston and Sahoo (Appl Math Lett 21:974-977, 2008). Springer Basel, 2014 d'Alembert's functional equation nationallicence involution nationallicence stability nationallicence Wilson's functional equation nationallicence Chung Jaeyoung Department of Mathematics, Kunsan National University, 573-701, Kunsan, Republic of Korea aut Sahoo Prasanna Department of Mathematics, University of Louisville, 40292, Louisville, KY, USA aut Aequationes mathematicae Springer Basel 89/3(2015-06-01), 749-763 0001-9054 89:3<749 2015 89 10 https://doi.org/10.1007/s00010-014-0262-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00010-014-0262-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chung Jaeyoung Department of Mathematics, Kunsan National University, 573-701, Kunsan, Republic of Korea aut NATIONALLICENCE 700 1- Sahoo Prasanna Department of Mathematics, University of Louisville, 40292, Louisville, KY, USA aut NATIONALLICENCE 773 0- Aequationes mathematicae Springer Basel 89/3(2015-06-01), 749-763 0001-9054 89:3<749 2015 89 10