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 {colon equals} {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.
Original language | English |
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Pages (from-to) | 538-546 |
Number of pages | 9 |
Journal | Applied Mathematics and Computation |
Volume | 185 |
Issue number | 1 |
DOIs | |
Publication status | Published - Feb 1 2007 |
All Science Journal Classification (ASJC) codes
- Computational Mathematics
- Applied Mathematics