Ulam-Hyers Stability of Quadratic FunctionalEquation in Banach Space

Abstract

The study of stability involves the use of functional equations. Ulam [14] proposed stability concerns of functional equations involving group homomorphisms in 1940. Under the presumption that groups are Banach spaces, Hyers [8] responded positively to Ulam's query regarding additive groups in 1941.Aoki [2] and Rassias[12] extended 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.