Strong convergence theorems for variational inequality problems and fixed point problems in uniformly smooth and uniformly convex Banach spaces

Strong convergence theorems for variational inequality problems and fixed point problems in uniformly smooth and uniformly convex Banach spaces

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Article ID: iaor20134148
Volume: 56
Issue: 4
Start Page Number: 1529
End Page Number: 1542
Publication Date: Aug 2013
Journal: Journal of Global Optimization
Authors: ,
Keywords: global convergence, mapping, fixed point theory
Abstract:

In this paper, we introduce a new iterative algorithm for finding a common element of the set of solutions of a general variational inequality problem for finite inverse‐strongly accretive mappings and the set of common fixed points for a nonexpansive mapping in a uniformly smooth and uniformly convex Banach space. We obtain a strong convergence theorem under some suitable conditions. Our results improve and extend the recent ones announced by many others in the literature.

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