Functional equations and inequalities in paranormed spaces

[摘要] Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of an additive functional equation, a quadratic functional equation, a cubic functional equation and a quartic functional equation in paranormed spaces. Furthermore, we prove the Hyers-Ulam stability of functional inequalities in paranormed spaces by using the fixed point method and the direct method. MSC:35A17, 47H10, 39B52, 39B72.

[学科分类] 数学（综合）

[关键词] Jordan-von Neumann functional equation;Hyers-Ulam stability;paranormed space;fixed point;functional equation;functional inequality