Abstract—One of the essential researches in mathematics is the study of functional equations, which originated in problems related to applied mathematics. Among those was the question concerning a general solution and a stability result of the functional equation, exceptionally fundamental equation in the theory of functional equations related to the Cauchy functional equation or additive functional equation. Nowadays, the number of mathematics papers concerning the stability results for many functional equations on normed spaces and non-Archimedean normed spaces via the direct method is still increasing. The fixed point theorem is an innovative tool to prove the stability result of the functional equation. Moreover, the stability result of the Euler-Lagrange-Jensen k-cubic functional equation was investigated for a mapping from a normed space to a Banach space. In this work, we prove the Hyers-Ulam stability for the Euler-Lagrange-Jensen k-cubic functional equation on generalized non-Archimedean normed spaces by using the fixed point method. Also, we can obtain the stability results of the Euler-Lagrange-Jensen k-cubic functional equation in the sense of Banach space from our main results.

Index Terms—Cubic functional equation, Euler-Lagrange-Jensen functional equation, Hyers-Ulam stability, non-Archimedean normed spaces.

Anurak Thanyacharoen is with Department of Mathematics, Faculty of Science and Technology, Muban Chombueng Rajabhat University, Ratchaburi 70150, Thailand (email: ake_poiuy@yahoo.com).
Wutiphol Sintunavarat is with Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Phatumthani 12120, Thailand.

Cite: Anurak Thanyacharoen, Wutiphol Sintunavarat, "Hyers-Ulam Stability of Euler-Lagrange-Jensen k-Cubic Functional Equations on Generalized Non-Archimedean Normed Spaces," International Journal of Applied Physics and Mathematics vol. 10, no. 2, pp. 73-80, 2020.

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