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Bull. Korean Math. Soc. 2010; 47(3): 503-511

Printed May 1, 2010

https://doi.org/10.4134/BKMS.2010.47.3.503

Copyright © The Korean Mathematical Society.

Browder's type strong convergence theorem for $S$-nonexpansive mappings

Jong Kyu Kim, Daya Ram Sahu, and Sajid Anwar

Kyungnam University, Banaras Hindu university, and Anjuman College of Engineering and Technology

Abstract

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We prove a common fixed point theorem for $S$-contraction mappings without continuity. Using this result we obtain an approximating curve for $S$-nonexpansive mappings in a Banach space and prove Browder's type strong convergence theorem for this approximating curve. The demiclosedness principle for $S$-nonexpansive mappings is also established.

Keywords: demicontinuity, $R$-weakly commutativity, $S$-contraction mapping, $S$-nonexpansive mapping

MSC numbers: 47H09, 46B20, 47H10, 54H25

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