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Strong Convergence of Modified Iteration Processes for Relatively Nonexpansive Mappings

Kim, Tae-Hwa;Lee, Hwa-Jung

  • Received : 2007.05.30
  • Published : 2008.12.31

Abstract

Motivated and inspired by ideas due to Matsushida and Takahashi [J. Approx. Theory 134(2005), 257-266] and Martinez-Yanes and Xu [Nonlinear Anal. 64(2006), 2400-2411], we prove some strong convergence theorems of modified iteration processes for a pair (or finite family) of relatively nonexpansive mappings in Banach spaces, which improve and extend the corresponding results of Matsushida and Takahashi and Martinez-Yanes and Xu in Banach and Hilbert spaces, repectively.

Keywords

strong convergence;modified Ishikawa's iteration;relatively nonexpansive mapping;nonexpansive mappings

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