Stability of a Quadratic-Reciprocal Functional Equation: Direct Method - Karthikeyan, S.; Suresh, M.; Priya, V. Banu; Palani, P. (Communications in Mathematics and Applications, 2023)
In this paper, we establish the Hyers-Ulam, Hyers-Ulam-Rassias, generalized Hyers-Ulam-Rassias, and Rassias stability results of the quadratic-reciprocal functional equation:\begin{align*}f(x+y)=\frac{f(x)f(y)}{f(x)+f(y)+2\sqrt{f(x)f(y)}}\end{align*} connected with fuzzy homomorphisms and fuzzy derivations between fuzzy Banach algebras using direct method.
Keywords: Quadratic reciprocal functional equation; Ulam-Hyers stability; Fuzzy Banach algebra