Stability of Quartic Functional Equation in Modular Spaces via Hyers and Fixed-Point Methods
Syed Abdul Mohiuddine,
Kandhasamy Tamilvanan,
Mohammad Mursaleen,
Trad Alotaibi
Affiliations
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
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 Δb-condition and without using both the Δb-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.
