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

• Published in: Mathematics (Basel) Vol. 11; no. 3; p. 681
• Main Authors: Agilan, P., Almazah, Mohammed M. A., Julietraja, K., Alsinai, Ammar
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01-01-2023
• Subjects: additive functional equations; Additive functions; fixed point method; Fixed point theory; Functional equations; Fuzzy algorithms; Fuzzy logic; fuzzy normed spaces; Fuzzy systems; Mathematical research; random normed spaces; Stability; Stability analysis; Symmetry; Ulam–Hyers Stability; India
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math11030681

In this article, a new kind of bilateral symmetric additive type functional equation is introduced. One of the interesting characteristics of the equation is the fact that it is ideal for investigating the Ulam–Hyers stabilities in two prominent normed spaces, namely fuzzy and random normed spaces simultaneously. This article analyzes the proposed equation in both spaces. The solution of this equation exhibits the property of symmetry, that is, the left of the object becomes the right of the image, and vice versa. Additionally, the stability results of this functional equation are determined in fuzzy and random normed spaces using direct and fixed point methods.