Ulam Stability of a Quartic Functional Equation - Abasalt Bodaghi; Idham Arif Alias; Mohammad Hosein Ghahramani (Abstract and Applied Analysis)
The oldest quartic functional equation was introduced by J. M. Rassias in (1999), and then was employed by other authors. The functional equation 𝑓(2𝑥+𝑦)+𝑓(2𝑥−𝑦)=4𝑓(𝑥+𝑦)+4𝑓(𝑥−𝑦)+24𝑓(𝑥)−6𝑓(𝑦) is called a quartic functional equation, all of its solution is said to be a quartic function. In the current paper, the Hyers-Ulam stability and the superstability for quartic functional equations are established by using the fixed-point alternative theorem.