Open Access Research Article

On Equivalence of Some Iterations Convergence for Quasi-Contraction Maps in Convex Metric Spaces

Zhiqun Xue1*, Guiwen Lv1 and BE Rhoades2

Author Affiliations

1 Department of Mathematics and Physics, Shijiazhuang Railway University, Shijiazhuang 050043, China

2 Department of Mathematics, Indiana University, Bloomington, IN 47405-7106, USA

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Fixed Point Theory and Applications 2010, 2010:252871  doi:10.1155/2010/252871

Published: 19 September 2010

Abstract

We show the equivalence of the convergence of Picard and Krasnoselskij, Mann, and Ishikawa iterations for the quasi-contraction mappings in convex metric spaces.