On the strong convergence theorems by the hybrid method for a family of mappings in uniformly convex Banach spaces

Document Type: Research Articles

Authors

1 Department of Mathematics, Islamic Azad University, Savadkooh Branch, Savadkooh, Iran.

2 Department of Mathematics, Islamic Azad University, Sari Branch, Sari, Iran.

3 Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar, Iran.

Abstract

Some algorithms for nding common xed point of a family of mappings is
constructed. Indeed, let C be a nonempty closed convex subset of a uniformly
convex Banach space X whose norm is Gateaux di erentiable and let {Tn} be
a family of self-mappings on C such that the set of all common fixed points
of {Tn} is nonempty. We construct a sequence {xn} generated by the hybrid
method and also we give the conditions of {Tn} under which {xn} converges
strongly to a common xed point of {Tn}.

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