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

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 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.

Keywords

• fixed-point method
• quartic functional equation
• Fatou property
• Hyers-Ulam stability
• Δb-condition