Approximation of fixed points of multifunctions in partial metric spaces

Abstract

Recently, Reich and Zaslavski [S. Reich and A.J. Zaslavski, Convergence of Inexact Iterative Schemes for Nonexpansive Set-Valued Mappings, Fixed Point Theory Appl. 2010 (2010), Article ID 518243, 10 pages] have studied a new inexact iterative scheme for fixed points of contractive multifunctions. In this paper, using the partial Hausdorff metric introduced by Aydi et al., we prove an analogous to a result of Reich and Zaslavski for contractive multifunctions in the setting of partial metric spaces. An example is given to illustrate our result.