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

P. Agilan (), Mohammed M. A. Almazah, K. Julietraja and Ammar Alsinai
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P. Agilan: Department of Mathematics, St. Joseph’s College of Engineering, OMR, Chennai 600119, Tamil Nadu, India
Mohammed M. A. Almazah: Department of Mathematics, College of Sciences and Arts (Muhyil), King Khalid University, Muhyil 61421, Saudi Arabia
K. Julietraja: Department of Mathematics, St. Joseph’s College of Engineering, OMR, Chennai 600119, Tamil Nadu, India
Ammar Alsinai: Department of Mathematics, University of Mysore, Manasagangotri, Mysore 570015, Karnataka, India

Mathematics, 2023, vol. 11, issue 3, 1-19

Abstract: 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.

Keywords: random normed spaces; fuzzy normed spaces; additive functional equations; Ulam–Hyers Stability; fixed point method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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