On the stability of the linear mapping in Banach spaces

Abstract

Let E 1 , E 2 {E_1},{E_2} be two Banach spaces, and let f : E 1 → E 2 f:{E_1} \to {E_2} be a mapping, that is “approximately linear". S. M. Ulam posed the problem: “Give conditions in order for a linear mapping near an approximately linear mapping to exist". The purpose of this paper is to give an answer to Ulam’s problem.