caa a22 4500 60620072X CHVBK 20210128100945.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s00025-014-0404-4 doi (NATIONALLICENCE)springer-10.1007/s00025-014-0404-4 Superstability of an Exponential Equation in $${{C^*}}$$ C ∗ -Algebras [Elektronische Daten] [Gwang Kim, Choonkil Park] The aim of this paper is to prove the superstability of the following functional equations $$f\left(\frac{x+y}{m}\right)^m \,=\, g(x)h(y),$$ f x + y m m = g ( x ) h ( y ) , where $${f, g, h: V^{2} \to A}$$ f , g , h : V 2 → A are unknown mappings and m is a fixed positive integer. Here V is a vector space, and A is a unital normed algebra. Furthermore, we prove the superstability of the following generalized Pexider exponential equation $$f\left(\frac{x+y}{r}\right)^r = g(x)h(y),$$ f x + y r r = g ( x ) h ( y ) , where $${f, g, h: V^{2}\to I(A)\cap A^+}$$ f , g , h : V 2 → I ( A ) ∩ A + are unknown mappings and r is a fixed nonzero rational number. Here V is a vector space, I(A) is the set of all invertible elements in a commutative unital C *-algebra A and $${A^+}$$ A + is the positive cone of A. Springer Basel, 2014 Hyers-Ulam stability nationallicence superstability nationallicence $${C^*}$$ C ∗ -Algebra nationallicence generalized Pexider exponential equation nationallicence Kim Gwang Department of Mathematics, Kangnam University, 446-702, Yongin, Gyeonggi, Republic of Korea aut Park Choonkil Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, 133-791, Seoul, Republic of Korea aut Results in Mathematics Springer Basel 67/1-2(2015-02-01), 197-205 1422-6383 67:1-2<197 2015 67 25 https://doi.org/10.1007/s00025-014-0404-4 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/s00025-014-0404-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kim Gwang Department of Mathematics, Kangnam University, 446-702, Yongin, Gyeonggi, Republic of Korea aut NATIONALLICENCE 700 1- Park Choonkil Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, 133-791, Seoul, Republic of Korea aut NATIONALLICENCE 773 0- Results in Mathematics Springer Basel 67/1-2(2015-02-01), 197-205 1422-6383 67:1-2<197 2015 67 25