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
SN - 1687-1820
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
IS - 2
ER -