Stability of Quartic Functional Equation in Modular Spaces via Hyers and Fixed-Point Methods

Syed Abdul Mohiuddine, Kandhasamy Tamilvanan, Mohammad Mursaleen and Trad Alotaibi
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Syed Abdul Mohiuddine: Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Kandhasamy Tamilvanan: Department of Mathematics, School of Advanced Sciences, Kalasalingam Academy of Research and Education, Srivilliputhur, Virudhunagar 626126, Tamil Nadu, India
Mohammad Mursaleen: Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung 40402, Taiwan
Trad Alotaibi: Department of Mathematics, College of Science, Taif University, Taif 21944, Saudi Arabia

Mathematics, 2022, vol. 10, issue 11, 1-22

Abstract: In this work, we introduce a new type of generalised quartic functional equation and obtain the general solution. We then investigate the stability results by using the Hyers method in modular space for quartic functional equations without using the Fatou property, without using the Δ b -condition and without using both the Δ b -condition and the Fatou property. Moreover, we investigate the stability results for this functional equation with the help of a fixed-point technique involving the idea of the Fatou property in modular spaces. Furthermore, a suitable counter example is also demonstrated to prove the non-stability of a singular case.

Keywords: fixed-point method; quartic functional equation; Fatou property; Hyers-Ulam stability; ?b-condition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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