Intuitionistic Fuzzy Stability of an Euler–Lagrange Symmetry Additive Functional Equation via Direct and Fixed Point Technique (FPT)

Abstract

In this article, a new class of real-valued Euler–Lagrange symmetry additive functional equations is introduced. The solution of the equation is provided, assuming the unknown function to be continuous and without any regularity conditions. The objective of this research is to derive the Hyers–Ulam–Rassias stability (HURS) in intuitionistic fuzzy normed spaces (IFNS) by applying the classical direct method and fixed point techniques (FPT). Furthermore, it is proven that the Euler–Lagrange symmetry additive functional equation and the control function, which is the IFNS of the sums and products of powers of norms, is stable. In addition, a few examples where the solution of this equation can be applied in Fourier series and Fourier transforms are demonstrated.

Classical and Fixed Point Approach to the Stability Analysis of a Bilateral Symmetric Additive Functional Equation in Fuzzy and Random Normed Spaces

“…for all U 1 , U 2 , U 3 ∈ F * and all R > 0. Using (29) and (A 5 ) in (30), the following result is derived:…”

Development p, q, r–Spherical Fuzzy Einstein Aggregation Operators: Application in Decision-Making in Logo Design

“…In addition, fuzzy sets are useful in dealing with linguistic factors as they allow for the introduction of qualitative judgements and subjective preferences into decision-making processes. Overall, using fuzzy sets improves MCDM's flexibility and resilience in dealing with the complexities and uncertainties that arise in real-world decision scenarios [15][16][17][18]. FSs represent partial membership using a single degree of membership (MD), whereas Intuitionistic Fuzzy Sets (IFSs) [19] introduce the concept of hesitation, which provides a more elaborate representation of uncertainty by taking into account both membership and non-membership, as well as a degree of hesitation.…”