Journal of Convex Analysis 18 (2011), No. 2, 465--487
Copyright Heldermann Verlag 2011
Alternative Iterative Methods for Nonexpansive Mappings, Rates of Convergence and Applications
Vittorio Colao
Dip. di Matematica, Università della Calabria, 87036 Arcavacata di Rende, Italy
colao@mat.unical.it
Laurentiu Leustean
Fachbereich Mathematik, Technische Universität, Schlossgartenstrasse 7, 64289 Darmstadt, Germany
and: Institute of Mathematics "Simion Stoilow", Romanian Academy, Calea Grivitei 21, 010702 Bucharest, Romania
Genaro López
Dep. de Análisis Matemático, Universidad de Sevilla, Apdo. 1160, 41080 Sevilla, Spain
glopez@us.es
Victoria Martín-Márquez
Dep. de Análisis Matemático, Universidad de Sevilla, Apdo. 1160, 41080 Sevilla, Spain
victoriam@us.es
Alternative iterative methods for a nonexpansive mapping in a Banach space are proposed and proved to be convergent to a common solution to a fixed point problem and a variational inequality. Rates of asymptotic regularity for such iterations are given using proof-theoretic techniques. Some applications of the convergence results are presented.
Keywords: Nonexpansive mapping, iterative algorithm, fixed point, viscosity approximation, uniformly smooth Banach space, rates of asymptotic regularity, proof mining, variational inequality, accretive operator.
MSC: 47H06, 47H09, 47H10, 47J20, 03F60
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