Fixed point technique: Hyers-Ulam stability results deriving from cubic mapping in fuzzy normed spaces

Authors

  • Dr. N. Vijaya
  • Dr. P. Suganthi
  • Ebenesar Anna Bagyam
  • Tamilvanan K R.M.K. Engineering College
  • Dr. N. Prabaharan

Keywords:

fuzzy normed spaces, Ulam stability, cubic mapping.

Abstract

In this work, we introduce a novel finite-dimensional cubic functional equation \[ \begin{aligned} \phi\Big(\sum_{a=1}^{l}a n_{a}\Big)=\sum_{1 \leq a < b < c \leq l}\phi\Big(a n_{a}+b n_{b}+c n_{c}\Big) & +(3-l)\sum_{1 \leq a < b \leq l}\phi\Big(a n_{a}+b n_{b}\Big)\\ & +\Big(\frac{(l^{2}-5l+6)}{2}\Big)\sum_{a=0}^{l-1}(a+1)^{3}\phi(n_{a+1}) \end{aligned} \] 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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Published

14-11-2024

How to Cite

N, V., P, S., Anna Bagyam, E. ., K, T., & N, . P. (2024). Fixed point technique: Hyers-Ulam stability results deriving from cubic mapping in fuzzy normed spaces. Communications in Mathematics and Applications, 15(2). Retrieved from http://rgnpublications.com/journals/index.php/cma/article/view/2679

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Section

Research Article