On the strong convergence theorems by the hybrid method for a family of mappings in uniformly convex Banach spaces
محورهای موضوعی : Applied Mathematics
M. Salehi
1
(
Department of Mathematics, Islamic Azad University, Savadkooh Branch, Savadkooh, Iran.
)
V. Dadashi
2
(
Department of Mathematics, Islamic Azad University, Sari Branch, Sari, Iran.
)
M. Roohi
3
(
Department of Mathematics, Faculty of Basic Sciences,
University of Mazandaran, Babolsar, Iran.
)
کلید واژه: Hybrid method, Common xed point, Iterative algorithm, Uniformly con- vex Banach space,
چکیده مقاله :
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 di erentiable 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}.
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 di erentiable 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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