Additive and quadratic functional inequalities in non-Archimedean normed spaces

Abstract

In this paper, we solve the additive functional inequality and the quadratic functional inequality in normed spaces.Moreover, we prove the Hyers-Ulam stability of the functional inequalities (1) and (2) in Banach spaces. Furthermore, we investigate the additive functional inequality in non-Archimedean normed spaces. Moreover, we prove the Hyers-Ulam stability of the functional inequalities (3) and (4) in non-Archimedean Banach spaces. ⓒ 2014 Jung Rye Lee, Choonkil Park and Dong Yun Shin.