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JP Journal of Fixed Point Theory and Applications

Abstract:
Let C be a closed convex subset of a 2-uniformly Banach space E with the best smooth constant K and

be a k-strict pseudo-contraction on C with a fixed point, for some

Given an initial guess

consider the Mann’s algorithm

It is proved that if the control sequence

is chosen so that

and

then the Mann iterative sequence

converges weakly to a fixed point of T.

Keywords and phrases: weak convergence, strict pseudo-contractive mapping, fixed point, uniformly smooth Banach spaces.

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P-ISSN: 0973-4228

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