Stability of a Quadratic-Reciprocal Functional Equation: Direct Method

S. Karthikeyan; M. Suresh; V. Banu Priya; P. Palani

doi:10.26713/cma.v14i5.2224

Authors

S. Karthikeyan Department of Mathematics, R.M.K. Engineering College, Kavaraipettai 601206, Tamil Nadu, India https://orcid.org/0000-0002-7639-8858 (unauthenticated)
M. Suresh Department of Mathematics, R.M.D. Engineering College, Kavaraipettai 601206, Tamil Nadu, India https://orcid.org/0000-0003-1438-1775 (unauthenticated)
V. Banu Priya Department of Mathematics, R.M.K. College of Engineering and Technology, Puduvoyal 601206, Tamil Nadu, India
P. Palani Department of Mathematics, Government Arts and Science College for Women, Karimangalam 635111, Tamil Nadu, India https://orcid.org/0009-0006-2591-7992 (unauthenticated)

DOI:

https://doi.org/10.26713/cma.v14i5.2224

Keywords:

Quadratic reciprocal functional equation, Ulam-Hyers stability, Fuzzy Banach algebra

Abstract

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.

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