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.
Highlights
Wang et al [17] showed the stability of a mixed type cubic–quartic functional equation in 2-Banach spaces
The main purpose of this paper is to investigate the Hyers–Ulam stability of (2) in fuzzy normed spaces with the help of direct and fixed point methods
We have introduced a new type of quartic functional equation and have derived its general solution
Summary
Many authors have investigated the functional equations in fuzzy normed linear spaces (See e.g., [3,4,5,6,7]). Derived the general solution of (1) and examined its stability results in Banach spaces. Eshaghi Gordji et al [19] investigated the stability of mixed type quartic–cubic–quadratic functional equations in non-Archimedean normed spaces. Lee et al [21] investigated the quartic functional equations in the space of generalized functions. Wang et al [17] showed the stability of a mixed type cubic–quartic functional equation in 2-Banach spaces. The main purpose of this paper is to investigate the Hyers–Ulam stability of (2) in fuzzy normed spaces with the help of direct and fixed point methods. (iii) d(q, b) ≤ 1−1 L d(q, Γq), q ∈ F
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