Approximations for fixed points of \(\phi\)-hemicontractive mappings by the Ishikawa iterative process with mixed errors. (English) Zbl 1003.47052
Let \(X\) be a real uniformly smooth Banach space, \(K\) be a nonempty closed convex subset of \(X\) and \(T: K\to K\) be a generalized Lipschitzian and hemicontractive mapping. It is shown that the Ishikawa iterative process with mixed errors converges strongly to the unique fixed point of the mapping \(T\). As consequences, several new strong convergence results are deduced and some known results are improved.
Reviewer: Jürgen Appell (Würzburg)
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H10 | Fixed-point theorems |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
Keywords:
generalized Lipschitzian and hemicontractive mapping; Ishikawa iterative process with mixed errorsReferences:
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