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In this paper, we investigate the stabillty for the generalized logarithmic functional equation. By using the fixed point method of Brzdȩk and Ciepliński [‘On a fixed point theorem in 2-Banach spaces and some of its applications’, Acta Math. Scientia, 38(2), 377-390], the generalized Hyers-Ulam stability results for the generalized logarithmic functional equation are proved. Our results generalize, extend and complement some earlier classical results concerning the stability of the logarithmic functional equations. In addition, the stability of logarithmic functional equation in 2-Banach spaces can be derived from our main results.

On New Approximations of the Generalized Logarithmic Functional Equation in 2-Banach Spaces