LAUSR

In this work, we apply the Brzdęk and Ciepliński’s fixed point theorem to investigate new stability results for the generalized Cauchy functional equation of the form $$f(ax+by)=af(x)+bf(y),$$ f ( a x + b y ) = a f ( x ) + b f ( y ) , where a , b ∈ ℕ and f is a mapping from a commutative group ( G , +) to a 2-Banach space ( Y , ∥ ·, · ∥). Our results are generalizations of main results of Brzdęk and Ciepliński [J Brzdęk, K Ciepliński. On a fixed point theorem in 2-normed spaces and some of its applications. Acta Mathematica Scientia, 2018, 38B (2): 377–390].