Non-Archimedean stability of a generalized reciprocal-quadratic functional equation in several variables by direct and fixed point methods

Abstract

This study is aimed to determine various stabilities of a generalized reciprocal-quadratic functional equation of the form r (Σpj=1 βjuj) = Πpj=1 r (uj) [Σpj=1 βj Πpk=1,k≠j √r(uk)] 2 connected with Ulam, Hyers, T. M. Rassias, J. M. Rassias and Gavruta in non-Archimedean fields, where βj≠0; j = 1,2,..., p are arbitrary real numbers and 0 < β1+β2+...+βp = Σpj=1 βj=β≠1 in non-Archimedean fields by direct and fixed point methods.