کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4633377 | 1340669 | 2008 | 7 صفحه PDF | دانلود رایگان |
Let E be a uniformly convex Banach space with a uniformly Gâteaux differentiable norm, K a nonempty closed convex subset of E , T:K→KT:K→K an asymptotically nonexpansive mapping with sequence {kn}⊂[1,∞),limn→∞kn=1{kn}⊂[1,∞),limn→∞kn=1. Let {αn}⊂(0,1){αn}⊂(0,1) be such that limn→∞αn=0,limn→∞kn-1αn=0 and f be a contraction on K . Under suitable conditions, we show the existence of a sequence {zn}{zn} satisfying the relation zn=αnf(zn)+(1-αn)Tnznzn=αnf(zn)+(1-αn)Tnzn, and prove that {zn}{zn} converges strongly to the fixed point of T, which solves some variational inequality, provided T is asymptotically regular. As an application, we prove that the iterative process defined by x0∈Kx0∈K, xn+1≔αnf(xn)+βnxn+γnTnxnxn+1≔αnf(xn)+βnxn+γnTnxn, converges strongly to the same fixed point of T.
Journal: Applied Mathematics and Computation - Volume 203, Issue 1, 1 September 2008, Pages 171–177