Strong convergence of the composite Halpern iteration |
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Authors: | Xiaolong Qin Yongfu Su |
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Institution: | a Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China b Department of Mathematics, Gyeongsang National University, Chinju 660-701, Republic of Korea c Department of Mathematics, Shijiazhuang University, Shijiazhuang 050035, China |
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Abstract: | Let C be a closed convex subset of a uniformly smooth Banach space E and let T:C→C be a nonexpansive mapping with a nonempty fixed points set. Given a point u∈C, the initial guess x0∈C is chosen arbitrarily and given sequences , and in (0,1), the following conditions are satisfied:- (i)
- ;
- (ii)
- αn→0, βn→0 and 0<a?γn, for some a∈(0,1);
- (iii)
- , and . Let be a composite iteration process defined by
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Keywords: | Iteration scheme Sunny and nonexpansive retraction Nonexpansive mapping Banach space |
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