Approximation methods for common fixed points for a countable family of nonexpansive mappings |
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Authors: | CE Chidume CO Chidume |
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Institution: | a The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy b Department of Mathematics and Statistics, Auburn University, Auburn, AL, United States c Mathematics Department, Wesley College, Dover, DE, United States |
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Abstract: | Let E=Lp or lp space, 1<p<∞. Let K be a closed, convex and nonempty subset of E. Let be a family of nonexpansive self-mappings of K. For arbitrary fixed δ∈(0,1), define a family of nonexpansive maps by Si?(1−δ)I+δTi where I is the identity map of K. Let . It is proved that the iterative sequence {xn} defined by: x0∈K,xn+1=αnu+∑i≥1σi,tnSixn,n≥0 converges strongly to a common fixed point of the family where {αn} and {σi,tn} are sequences in (0,1) satisfying appropriate conditions, in each of the following cases: (a) E=lp,1<p<∞, and (b) E=Lp,1<p<∞ and at least one of the maps Ti’s is demicompact. Our theorems extend the results of P. Maingé, Approximation methods for common fixed points of nonexpansive mappings in Hilbert space, J. Math. Anal. Appl. 325 (2007) 469-479] from Hilbert spaces to lp spaces, 1<p<∞. |
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Keywords: | 47H09 47J25 |
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