Iterative algorithm for multi-valued pseudocontractive mappings in Banach spaces |
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Authors: | Eric U Ofoedu Habtu Zegeye |
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Institution: | a Department of Mathematics, Nnamdi Azikiwe University, P.M.B. 5025, Awka, Anambra State, Nigeria b Bahir Dar University, P.O. Box 859, Bahir Dar, Ethiopia |
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Abstract: | Let D be nonempty open convex subset of a real Banach space E. Let be a continuous pseudocontractive mapping satisfying the weakly inward condition and let be fixed. Then for each t∈(0,1) there exists satisfying yt∈tTyt+(1−t)u. If, in addition, E is reflexive and has a uniformly Gâteaux differentiable norm, and is such that every closed convex bounded subset of has fixed point property for nonexpansive self-mappings, then T has a fixed point if and only if {yt} remains bounded as t→1; in this case, {yt} converges strongly to a fixed point of T as t→1−. Moreover, an explicit iteration process which converges strongly to a fixed point of T is constructed in the case that T is also Lipschitzian. |
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Keywords: | Hausdorff metric Nonexpansive mappings Pseudocontractive mappings Weakly inward Uniform Gâ teuax differentiable norms |
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