Strong convergence theorems for uniformly continuous pseudocontractive maps |
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Authors: | CE Chidume A Udomene |
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Institution: | a The Abdus Salam International Centre for Theoretical Physics, 34100 Trieste, Italy b Department of Mathematics/Statistics/Computer Science, University of Port Harcourt, PMB 5323 Port Harcourt, Nigeria |
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Abstract: | Let K be a nonempty closed convex subset of a real Banach space E and let be a uniformly continuous pseudocontraction. Fix any u∈K. Let {xn} be defined by the iterative process: x0∈K, xn+1:=μn(αnTxn+(1−αn)xn)+(1−μn)u. Let δ(?) denote the modulus of continuity of T with pseudo-inverse ?. If and {xn} are bounded then, under some mild conditions on the sequences n{αn} and n{μn}, the strong convergence of {xn} to a fixed point of T is proved. In the special case where T is Lipschitz, it is shown that the boundedness assumptions on and {xn} can be dispensed with. |
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Keywords: | Uniformly continuous maps Pseudocontractions f p p Banach spaces Uniformly Gâ teaux differentiable norm |
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