General solution and generalized Hyers-Ulam stability for additive functional equations

Volume 29, Issue 4, pp 343--355 https://doi.org/10.22436/jmcs.029.04.04

Publication Date: November 03, 2022 Submission Date: June 12, 2022 Revision Date: July 17, 2022 Accteptance Date: August 13, 2022

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Authors

S. S. Santra - Department of Mathematics, Applied Science Cluster, University of Petroleum and Energy Studies, Dehradun, Uttarakhand - 248007, India. M. Arulselvam - Government Arts College for Men, Krishnagiri-635 001, Tamil Nadu, India. D. Baleanu - Department of Mathematics and Computer Science, Faculty of Arts and Sciences, Ankaya University, Ankara, 06790 Etimesgut, Turkey. - Instiute of Space Sciences, Magurele-Bucharest, 077125 Magurele, Romania. - Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan, Republic of China. V. Govindan - Department of Mathematics, DMI St John The Baptist University Central, Mangochi-409, Cental Africa, Malawi. Kh. M. Khedher - Department of Civil Engineering, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia. - Department of Civil Engineering, High Institute of Technological Studies, Mrezgua University Campus, Nabeul 8000, Tunisia.

Abstract

In this paper, we introduce new types of additive functional equations and obtain the solutions to these additive functional equations. Furthermore, we investigate the Hyers-Ulam stability for the additive functional equations in fuzzy normed spaces and random normed spaces using the direct and fixed point approaches. Also, we will present some applications of functional equations in physics. Through these examples, we explain how the functional equations appear in the physical problem, how we use them to solve it, and we talk about solutions that are not used for solving the problem, but which can be of interest. We provide an example to show how functional equations may be used to solve geometry difficulties.

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Keywords

• Hyers-Ulam stability
• fuzzy normed space
• random normed space and fixed point

MSC

•  39B72
•  39B82

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