Stability of Functional Equation (1) using Fixed Point Method

Abstract

Hyers' theorem to include additive mappings and linear mappings, respectively, by taking into account an unbounded Cauchy difference  for all and. Gavruta [5] also presented Rassias generalization theorem, substituting a control function for. The concept of the Hyers-Ulam-Rassias stability of functional equations has been developed largely thanks to Rassias' publication. In 1982, Rassias [13] adopted the Rassias theorem [14]'s contemporary methodology, substituting the factor product of norms for the sum of norms.