Convergence theorems for implicit iteration process for a finite family of continuous pseudocontractive mappings |
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Authors: | Rudong Chen Yisheng Song |
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Institution: | a Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, PR China b Department of Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, PR China |
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Abstract: | In this paper, a necessary and sufficient conditions for the strong convergence to a common fixed point of a finite family of continuous pseudocontractive mappings are proved in an arbitrary real Banach space using an implicit iteration scheme recently introduced by Xu and Ori H.K. Xu, R.G. Ori, An implicit iteration process for nonexpansive mappings, Numer. Fuct. Anal. Optim. 22 (2001) 767-773] in condition αn∈(0,1], and also strong and weak convergence theorem of a finite family of strictly pseudocontractive mappings of Browder-Petryshyn type is obtained. The results presented extend and improve the corresponding results of M.O. Osilike M.O. Osilike, Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps, J. Math. Anal. Appl. 294 (2004) 73-81]. |
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Keywords: | Continuous pseudocontractive mappings Strictly pseudocontractive mappings Implicit iteration process Common fixed points |
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