QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN FUZZY NORMED SPACES

Abstract

In this paper, we solve the following quadratic rho-functional inequalities

N(f(x + y) + f(x + y) - 2f(x) - 2f(y),t) (0.1)

>= N (rho(2f (x+y/2) + 2f (x-y/2) - f(x) - f(y)), t)

where rho is a fixed real number with vertical bar rho vertical bar < 1, and

N (2f(x+y/2) + 2f(x-y/2) - f(x) - f(y), t) (0.2)

>= N (rho(f (x+y) + f (x-y) - 2f(x) - 2f(y)), t)

where rho is a fixed real number with vertical bar rho vertical bar < 1/2.

Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic functional inequalities (0.1) and (0.2) in fuzzy Banach spaces.