Ulam stability of an additive-quadratic functional equation in F-space and quasi-Banach spaces

2022/03/07 by Fu, Linlin, Liu, Qi, Li, Yongjin
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2203.03114

Abstract

By adopting the direct method and fixed point method, we prove that the Hyers-Ulam stability of the following additive-quadratic functional equation f(x+y, z+w)+f(x-y, z-w)-2 f(x, z)-2 f(x, w)=0 in β-homogeneous F-spaces and quasi-Banach spaces. There are some differences that we consider the target space with the β-homogeneous norm and quasi-norm. Overcoming the β-homogeneous norm and quasi-norm bottlenecks, we get some new results.

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