Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
841872 | Nonlinear Analysis: Theory, Methods & Applications | 2010 | 9 Pages |
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:KâK be a λ-strict pseudocontraction for some 0â¤Î»<1 with xââF(T):={xâK:Tx=x}â 0̸. For a fixed x0âK, define a sequence {xn} by xn+1=(1âαn)xn+αnTxn, where {αn} is a sequence in [0,1] satisfying the following conditions: (i) ân=0âαn=â; (ii) ân=0âαn2<â. 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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Authors
C.E. Chidume, Naseer Shahzad,