Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4636303 | Applied Mathematics and Computation | 2007 | 9 Pages |
Abstract
Let K be a closed convex subset of a Banach space E and let T : K → E be a continuous weakly inward pseudocontractive mapping. Then for t ∈ (0, 1), there exists a sequence {yt} ⊂ K satisfying yt = (1 − t)f(yt) + tT(yt), where f ∈ ΠK ≔ {f : K → K, a contraction with a suitable contractive constant}. Suppose further that F(T) ≠ ∅ and E is reflexive and strictly convex which has uniformly Gâteaux differentiable norm. Then it is proved that {yt} converges strongly to a fixed point of T which is also a solution of certain variational inequality. Moreover, an explicit iteration process which converges strongly to a fixed point of T and hence to a solution of certain variational inequality is constructed provided that T is Lipschitzian.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Habtu Zegeye, Naseer Shahzad, Tefera Mekonen,