Generalized Hyers-Ulam Stability of Quadratic Functional Inequality

Abstract

We establish the general solution of the functional inequality ‖ (−)+ (−)+ (−)−3 ()−3 ()−3 ()‖ ≤ ‖ (+ +)‖ and then investigate the generalized Hyers-Ulam stability of this inequality in Banach spaces and in non-Archimedean Banach spaces.

On the General Solution of a Quadratic Functional Equation and its Ulam Stability in Various Abstract Spaces

“…In recent years, there are many interesting results concerning these problems obtained by different authors [2,3,5,8,9,10,11,13,14,15,16,17,23].…”

Generalized Hyers-Ulam stability of cubic functional inequality

“…Park et al [23] have proved the generalized Hyers-Ulam stability of functional inequalities associated with Jordan-von Neumann type additive functional equations, and Y. Cho and H. Kim [3] have proved the generalized Hyers-Ulam stability of functional inequalities with Cauchy-Jensen additive mappings. Recently, H. Kim, K. Jun and E. Son [19] have established the generalized Hyers-Ulam stability of quadratic functional inequality in Banach spaces and in non-Archimedean Banach spaces.…”