Abstract—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.

Index Terms—Fixed point theorem, generalized logarithmic functional equation, Hyers-Ulam stability, 2-Banach spaces.

The authors are with Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12120, Thailand (email: Laddawan_Aiemsomboon@hotmail.com).

Cite: Laddawan Aiemsomboon, Wutiphol Sintunavarat, "On New Approximations of the Generalized Logarithmic Functional Equation in 2-Banach Spaces," International Journal of Applied Physics and Mathematics vol. 10, no. 2, pp. 88-95, 2020.

Copyright © 2020 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).