Stability of the Cauchy additive and quadratic type functional equation in non-Archimedean normed spaces (Q2844411)

The stability problem of functional equations originated from a question of Ulam in 1940, concerning the stability of group homomorphisms. In 1941, D. H. Hyers gave a first affirmative answer to the question for Banach spaces.NEWLINENEWLINE\textit{M. S. Moslehian} and \textit{T. M. Rassias} [Appl. Anal. Discrete Math. 1, No. 2, 325--334 (2007; Zbl 1257.39019)] discussed the Hyers-Ulam stability of the Cauchy equation NEWLINE\[NEWLINEf(x+y)=f(x)+f(y)NEWLINE\]NEWLINE and the quadratic functional equation NEWLINE\[NEWLINEf(x+y)+f(x-y)-2f(x)-2f(y)=0NEWLINE\]NEWLINE in non-Archimedean normed spaces.NEWLINENEWLINEIn the present paper, the authors investigate the stability problem of the functional equation NEWLINE\[NEWLINEf(x+y)+f(x-y)-2f(x)-f(y)-f(-y)=0NEWLINE\]NEWLINE in the non-Archimedean normed spaces.