TY - JOUR

T1 - Convergence theorems for a common fixed point of a finite family of nonself nonexpansive mappings

AU - Chidume, C. E.

AU - Zegeye, Habtu

AU - Shahzad, Naseer

PY - 2005/12/1

Y1 - 2005/12/1

N2 - Let K be a nonempty closed convex subset of a reflexive real Banach space E which has a uniformly Gâteaux differentiable norm. Assume that K is a sunny nonexpansive retract of E with Q as the sunny nonexpansive retraction. Let Ti: K → E, i = 1,..., r, be a family of nonexpansive mappings which are weakly inward. Assume that every nonempty closed bounded convex subset of K has the fixed point property for nonexpansive mappings. A strong convergence theorem is proved for a common fixed point of a family of nonexpansive mappings provided that Ti, i = 1, 2,..., r, satisfy some mild conditions.

AB - Let K be a nonempty closed convex subset of a reflexive real Banach space E which has a uniformly Gâteaux differentiable norm. Assume that K is a sunny nonexpansive retract of E with Q as the sunny nonexpansive retraction. Let Ti: K → E, i = 1,..., r, be a family of nonexpansive mappings which are weakly inward. Assume that every nonempty closed bounded convex subset of K has the fixed point property for nonexpansive mappings. A strong convergence theorem is proved for a common fixed point of a family of nonexpansive mappings provided that Ti, i = 1, 2,..., r, satisfy some mild conditions.

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U2 - 10.1155/FPTA.2005.233

DO - 10.1155/FPTA.2005.233

M3 - Article

AN - SCOPUS:33749552101

VL - 2005

SP - 233

EP - 241

JO - Fixed Point Theory and Algorithms for Sciences and Engineering

JF - Fixed Point Theory and Algorithms for Sciences and Engineering

SN - 1687-1820

IS - 2

ER -