QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN FUZZY NORMED SPACES

초록

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.

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