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

Jae Ug Jeong

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.

Keywords


Fixed point; inverse strongly accretive mapping; varia- tional inequality; nonexpansive mapping.

Subject classification

49J30, 49J40, 47J25, 49H09.

Sponsor(s)

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

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