Strong convergence of iterative methods by strictly pseudocontractive mappings in Banach spaces |
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Authors: | D.R. Sahu |
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Affiliation: | a Department of Mathematics, Banaras Hindu University, Varanasi-221005, Indiab Department of Mathematics, Babe?-Bolyai University, Cluj-Napoca, Kogalniceanu 1, 400084 Cluj-Napoca, Romania |
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Abstract: | In this paper we deal with fixed point computational problems by strongly convergent methods involving strictly pseudocontractive mappings in smooth Banach spaces. First, we prove that the S-iteration process recently introduced by Sahu in [14] converges strongly to a unique fixed point of a mapping T, where T is κ-strongly pseudocontractive mapping from a nonempty, closed and convex subset C of a smooth Banach space into itself. It is also shown that the hybrid steepest descent method converges strongly to a unique solution of a variational inequality problem with respect to a finite family of λi-strictly pseudocontractive mappings from C into itself. Our results extend and improve some very recent theorems in fixed point theory and variational inequality problems. Particularly, the results presented here extend some theorems of Reich (1980) [1] and Yamada (2001) [15] to a general class of λ-strictly pseudocontractive mappings in uniformly smooth Banach spaces. |
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Keywords: | 47J20 49J40 65J15 |
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