Korean J. Math. Vol. 23 No. 3 (2015) pp.409-425
DOI: https://doi.org/10.11568/kjm.2015.23.3.409

Strong convergence of an iterative algorithm for a modified system of variational inequalities and a finite family of nonexpansive mappings in Banach spaces

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Published: Sep 30, 2015
Keywords:
Fixed point, inverse strongly accretive mapping, varia- tional inequality, nonexpansive mapping.
Mathematics Subject Classification:
49J30, 49J40, 47J25, 49H09.

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Jae Ug Jeong
Department of Mathematics Dongeui University Busan 614-714, South Korea

Abstract

In this paper, a new iterative scheme based on the extra-gradient-like method for finding a common element of the set of fixed points of a finite family of nonexpansive mappings and the set of solutions of modified variational inequalities in Banach spaces. A strong convergence theorem for this iterative scheme in Banach spaces is established. Our results extend recent results announced by many others.


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Supporting Agencies

This work was supported by Dong-eui University Grant (2015AA049).

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