Work

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

Year: 2024

Type: article

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.

Source: Communications in Mathematics and Applications

DOI: 10.26713/cma.v15i2.2679

Authors: N. Vijaya, P. Suganthi, Ebenesar Anna Bagyam, Manivannan Balamurugan, N. Prabaharan, K. Tamilvanan

Institutions: Saveetha University, Karpagam Academy of Higher Education, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, R.M.D. Engineering College

Language: English

Topic: Functional Equations Stability Results

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4407059276

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