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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 \(n\geq 1\) 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 involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
46B20 Geometry and structure of normed linear spaces
47H10 Fixed-point theorems
65J15 Numerical solutions to equations with nonlinear operators
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