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Convergence theorems for asymptotically pseudocontractive mappings in the intermediate sense. (English) Zbl 1228.47065
Summary: We prove strong convergence of the Ishikawa scheme for uniformly $L$-Lipschitzian and asymptotically pseudocontractive mappings in the intermediate sense. No compactness assumption is imposed either on $T$ or $C$, and computation of intersection of closed convex sets ${C}_{n}$ and ${Q}_{n}$ for each $n\ge 1$ is not required. We also obtain convergence results in this direction for asymptotically strict pseudocontractive mappings in the intermediate sense. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.
##### MSC:
 47J25 Iterative procedures (nonlinear operator equations) 47H09 Mappings defined by “shrinking” properties 46B20 Geometry and structure of normed linear spaces 47H10 Fixed point theorems for nonlinear operators on topological linear spaces 65J15 Equations with nonlinear operators (numerical methods)
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