Browder's type strong convergence theorem for $S$-nonexpansive mappings
Bull. Korean Math. Soc. 2010 Vol. 47, No. 3, 503-511
https://doi.org/10.4134/BKMS.2010.47.3.503
Published online May 1, 2010
Jong Kyu Kim, Daya Ram Sahu, and Sajid Anwar
Kyungnam University, Banaras Hindu university, and Anjuman College of Engineering and Technology
Abstract : 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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