Article ID Journal Published Year Pages File Type
841872 Nonlinear Analysis: Theory, Methods & Applications 2010 9 Pages PDF
Abstract
Let E be a uniformly smooth real Banach space which is also uniformly convex and K be a nonempty closed convex subset of E. Let T:K→K be a λ-strict pseudocontraction for some 0≤λ<1 with x∗∈F(T):={x∈K:Tx=x}≠0̸. For a fixed x0∈K, define a sequence {xn} by xn+1=(1−αn)xn+αnTxn, where {αn} is a sequence in [0,1] satisfying the following conditions: (i) ∑n=0∞αn=∞; (ii) ∑n=0∞αn2<∞. Then, {xn} converges weakly to a fixed point of T. Furthermore, weak convergence theorems are proved for a common fixed point for a finite family of strict pseudocontractions.
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