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It is well-known that Mann’s algorithm fails to converge for Lipschitzian pseudocontractions and strong convergence of Ishikawa’s algorithm for Lipschitzian pseudocontractions have not been achieved without compactness assumption on pseudocontractive mapping T or underlying space C. A new algorithm, which couples Ishikawa algorithms with hybrid techniques for finding the fixed points of a Lipschitzian pseudocontractive mapping, is constructed in this paper. Strong convergence of the presented algorithm is shown without any compactness assumption.

Coupling Ishikawa algorithms with hybrid techniques for pseudocontractive mappings