Alternative Iterative Methods for Nonexpansive Mappings, Rates of Convergence and Applications

Vittorio Colao; Laurentiu Leustean; Genaro López; Victoria Martín-Márquez

Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

Nonexpansive mapping
iterative algorithm
fixed point
viscosity approximation
uniformly smooth Banach space
rates of asymptotic regularity
proof mining
variational inequality
accretive operator

Mathematics Subject Classification

47H06, 47H09, 47H10, 47J20, 03F60

Suggested citation

V. Colao, L. Leustean, G. López, V. Martín-Márquez. “Alternative Iterative Methods for Nonexpansive Mappings, Rates of Convergence and Applications.” Journal of Convex Analysis 18 (2011), No. 2, 465–487.