Strong convergence of modified Ishikawa iteration for two asymptotically nonexpansive mappings and semigroups |
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Authors: | Somyot Plubtieng Kasamsuk Ungchittrakool |
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Institution: | Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand |
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Abstract: | In this paper, we established strong convergence theorems for a common fixed point of two asymptotically nonexpansive mappings and for a common fixed point of two asymptotically nonexpansive semigroups by using the hybrid method in a Hilbert space. Moreover, we also proved a strong convergence theorem for a common fixed point of two nonexpansive mappings. Our results extend and improve the recent ones announced by Kim and Xu T.W. Kim, H.W. Xu, Strong convergence of modified Mann iteration for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal. 64 (2006) 1140–1152], Nakajo and Takahashi K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372–379], and many others. |
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Keywords: | Strong convergence Asymptotically nonexpansive mappings Asymptotically nonexpansive semigroups Common fixed points |
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