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Turkish Journal of Mathematics

DOI

10.3906/mat-0805-26

Abstract

Let T, A be operators with domains D(T) \subseteq D(A) in a normed space X. The operator A is called T-bounded if Ax \leq a x +b Tx for some a, b\geq 0 and all x \in D(T). If A has the Hyers--Ulam stability then under some suitable assumptions we show that both T and S: = A+T have the Hyers--Ulam stability. We also discuss the best constant of Hyers--Ulam stability for the operator S. Thus we establish a link between T-bounded operators and Hyers--Ulam stability.

First Page

143

Last Page

149

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Mathematics Commons

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