ON THE STABILITY OF THE LINEAR MAPPING IN 2-NORMED SPACES

Abstract

The stability problem for approximate homeomorphisms was posed by Ulam in the year 1940. One year later Hyers provided a partial solution of Ulam problem for mappings between Banach spaces. In the year 1978, Rassias introduced the concept of unbounded Cauchy difference and was able to prove the generalized Hyers-Ulam stability of the linear mapping between Banach spaces. This concept, that was introduced by Rassias, is known today with the terms Hyers-Ulam-Rassias stability or Cauchy-Rassias stability for functional equations. In the present paper a proof of a generalized version of the stability theorems of Hyers and Rassias is given for 2-normed spaces.