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

Subject Areas : Applied Mathematics

M. Salehi ¹ , V. Dadashi ² , M. Roohi ³

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.

Received: 2015-10-05 Accepted : 2015-10-05 Published : 2012-12-01

Keywords: Hybrid method, Common xed point, Iterative algorithm, Uniformly con- vex Banach space,

Abstract :

Some algorithms for nding common xed point of a family of mappings isconstructed. Indeed, let C be a nonempty closed convex subset of a uniformlyconvex Banach space X whose norm is Gateaux dierentiable and let {Tn} bea family of self-mappings on C such that the set of all common fixed pointsof {Tn} is nonempty. We construct a sequence {xn} generated by the hybridmethod and also we give the conditions of {Tn} under which {xn}convergesstrongly to a common xed point of {Tn}.

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