TY - JOUR

T1 - Iterative algorithm for multi-valued pseudocontractive mappings in Banach spaces

AU - Ofoedu, Eric U.

AU - Zegeye, Habtu

PY - 2010/12/1

Y1 - 2010/12/1

N2 - Let D be nonempty open convex subset of a real Banach space E. Let T:D→KC(E) be a continuous pseudocontractive mapping satisfying the weakly inward condition and let u∈D be fixed. Then for each t∈(0,1) there exists yt∈D satisfying yt∈tTyt+(1-t)u. If, in addition, E is reflexive and has a uniformly Gâteaux differentiable norm, and is such that every closed convex bounded subset of D has fixed point property for nonexpansive self-mappings, then T has a fixed point if and only if {yt} remains bounded as t→1; in this case, {yt} converges strongly to a fixed point of T as t→1-. Moreover, an explicit iteration process which converges strongly to a fixed point of T is constructed in the case that T is also Lipschitzian.

AB - Let D be nonempty open convex subset of a real Banach space E. Let T:D→KC(E) be a continuous pseudocontractive mapping satisfying the weakly inward condition and let u∈D be fixed. Then for each t∈(0,1) there exists yt∈D satisfying yt∈tTyt+(1-t)u. If, in addition, E is reflexive and has a uniformly Gâteaux differentiable norm, and is such that every closed convex bounded subset of D has fixed point property for nonexpansive self-mappings, then T has a fixed point if and only if {yt} remains bounded as t→1; in this case, {yt} converges strongly to a fixed point of T as t→1-. Moreover, an explicit iteration process which converges strongly to a fixed point of T is constructed in the case that T is also Lipschitzian.

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U2 - 10.1016/j.jmaa.2010.07.020

DO - 10.1016/j.jmaa.2010.07.020

M3 - Article

AN - SCOPUS:77955281324

VL - 372

SP - 68

EP - 76

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -