Abstract

In this paper, we present generalized stability results of refined quadratic functional equation \[ f(ax-by)=abf(x-y)+a(a-b)f(x)+b(b-a)f(y), \] for any fixed nonzero integer numbers \(a,b\in\mathbb{Z}\) with \(a\neq b\) in modular spaces. As results, we generalize stability results of a quadratic functional equation in [{K.-W. Jun, H.-M. Kim, J. Son, Functional Equations in Mathematical Analysis, \(\bf{2012}\) (2012), 153--164}].

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