CUBIC AND QUARTIC ρ-FUNCTIONAL INEQUALITIES IN FUZZY BANACH SPACES

Abstract

In this paper, we solve the following cubic rho-functional inequality

N(f (2x + y) + f(2x - y) - 2f(x + y) - 2f (x - y) - 12f(x) (0.1)

-rho(4f(x + y/2) + 4f(x - y/2) - f(x + y) - f(x - y) - 6f(x)),t) >= t/t + phi(x, y)

and the following quartic rho-functional inequality

N(f(2x + y) + f(2x - y) - 4f(x + y) - 4f(x - y) - 24f(x) + 6f(y) (0.2)

-rho(8f(x + y/2) + 8f(x - y/2) - 2f(x + y) - 2f(x - y) - 12f(x) + 3f(y)),t)

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

in fuzzy normed spaces, where. is a fixed real number with rho not equal 2.

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