Fuzzy Stability Results of Generalized Quartic Functional Equations

Abstract

In the present paper, we introduce a new type of quartic functional equation and examine the Hyers–Ulam stability in fuzzy normed spaces by employing the direct method and fixed point techniques. We provide some applications in which the stability of this quartic functional equation can be controlled by sums and products of powers of norms. In particular, we show that if the control function is the fuzzy norm of the product of powers of norms, the quartic functional equation is hyperstable.

Keywords

• quartic functional equation
• Hyers–Ulam stability
• fixed point
• fuzzy normed space