Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
843663 | Nonlinear Analysis: Theory, Methods & Applications | 2007 | 9 Pages |
Abstract
Let K be a nonempty closed convex subset of a real Banach space E. Let T:KâK be a generalized Lipschitz pseudo-contractive mapping such that F(T)â{xâK:Tx=x}â 0̸. Let {αn}nâ¥1,{λn}nâ¥1 and {θn}nâ¥1 be real sequences in (0,1) such that αn=o(θn),limnââλn=0 and λn(αn+θn)<1. From arbitrary x1âK, let the sequence {xn}nâ¥1 be iteratively generated by xn+1=(1âλnαn)xn+λnαnTxnâλnθn(xnâx1),nâ¥1. Then, {xn}nâ¥1 is bounded. Moreover, if E is a reflexive Banach space with uniformly Gâteaux differentiable norm and if ân=1âλnθn=â is additionally assumed, then, under mild conditions, {xn}nâ¥1 converges strongly to some xââF(T).
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Authors
C.E. Chidume, E.U. Ofoedu,