QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN FUZZY BANACH SPACES

Abstract

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

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

>= t/t + phi(x, y), (0.1)

where rho is a fixed real number with rho not equal 2, and

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

>= t/t+phi(x,y), (0.2)

where rho is a fixed real number with rho not equal 1/2.

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