Fixed Point Technique: Hyers-Ulam Stability Results Deriving From Cubic Mapping in Fuzzy Normed Spaces

N. Vijaya; P. Suganthi; Ebenesar Anna Bagyam; Manivannan Balamurugan; N. Prabaharan; K. Tamilvanan

doi:10.26713/cma.v15i2.2679

Authors

N. Vijaya Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Thandalam, Chennai 602105, Tamil Nadu, India https://orcid.org/0000-0002-1838-9347 (unauthenticated)
P. Suganthi Department of Mathematics, R.M.K. Engineering College, Kavaraipettai, Tiruvallur 601206, Tamil Nadu, India https://orcid.org/0000-0002-8251-9660 (unauthenticated)
Ebenesar Anna Bagyam Department of Mathematics, Karpagam Academy of Higher Education, Coimbatore 641021, Tamil Nadu, India https://orcid.org/0000-0002-9943-5893 (unauthenticated)
Manivannan Balamurugan Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, Tamil Nadu, India https://orcid.org/0000-0002-1143-2090 (unauthenticated)
N. Prabaharan Department of Mathematics, R.M.D. Engineering College, Kavaraipettai, Tiruvallur 601206, Tamil Nadu, India https://orcid.org/0000-0002-7364-2480 (unauthenticated)
K. Tamilvanan Department of Mathematics, R.M.K. Engineering College, Kavaraipettai, Tiruvallur 601206, Tamil Nadu, India https://orcid.org/0000-0002-4900-7604 (unauthenticated)

DOI:

https://doi.org/10.26713/cma.v15i2.2679

Keywords:

Fuzzy normed spaces, Ulam stability, Cubic mapping

Abstract

In this work, we introduce a novel finite-dimensional cubic functional equation
\begin{align*}
\phi\Bigg(\sum\limits_{a=1}^{l}a n_{a}\Bigg)&=\sum\limits_{1 \leq a < b < c \leq l}\phi(a n_{a}+b n_{b}+c n_{c})\\
&\quad +(3-l)\sum\limits_{1 \leq a < b \leq l}\phi(a n_{a}+b n_{b})\\
&\quad +\Bigg(\frac{(l^{2}-5l+6)}{2}\Bigg)\sum\limits_{a=0}^{l-1}(a+1)^{3}\phi(n_{a+1}),
\end{align*}
where $l \geq 4$ is an integer, and derive its general solution.\ The main purpose of this work is to examine the Hyers-Ulam stability of this functional equation in fuzzy normed spaces by means of direct approach and fixed point approach.

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