Explicit iteration methods for a~class of variational inequalities in Banach spaces
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2015), pp. 19-26.

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In this paper, in order to solve a variational inequality problem over the set of common fixed points of an infinite family of nonexpansive mappings on real reflexive and strictly convex Banach spaces with a uniformly Gâteaux differentiable norm, we introduce two new explicit iteration methods.
Keywords: nonexpansive mapping, fixed point, variational inequality.
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Nguyen Buong; Nguen Thi Hong Phuong; Nguyen Thi Thu Thuy. Explicit iteration methods for a~class of variational inequalities in Banach spaces. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2015), pp. 19-26. http://geodesic.mathdoc.fr/item/IVM_2015_10_a1/

[1] Buong Ng., Phuong Ng. Th. H., “Regularization methods for a class of variational inequalities in Banach spaces”, Comput. Math. and Math. Physics, 52:11 (2012), 1487–1496 | DOI | MR

[2] Buong Ng., Phuong Ng. Th. H., “Strong convergence to solution for a class of variational inequalities in Banach spaces by implicit iteration methods”, J. Optim. Theory Appl., 159 (2013), 399–411 | DOI | MR | Zbl

[3] Buong Ng., Duong L. Th., “An explicit iterative algorithm for a class of variational inequalities in Hilbert spaces”, J. Optim. Theory Appl., 151:5 (2011), 513–524 | DOI | MR | Zbl

[4] Takahashi W., “Weak and strong convergence theorems for families of nonexpansive mappings and their applications”, Ann. Univ. Maria Curie-Sklodowska Sect. A, 51 (1997), 277–292 | MR | Zbl

[5] Yao Y., Noor M. A., Liou Y. C., “A new hybrid iterative algorithm for variational inequalities”, Appl. Math. Comput., 216 (2010), 822–829 | DOI | MR | Zbl

[6] Wang Sh., “Convergence and weaker control conditions for hybrid iterative algorithms”, Fixed Point Theory and Appl., 2011 (2011) | DOI | MR

[7] Ceng L. C., Ansari Q. H., Yao J. Ch., “Mann-type steepest-descent and modified hybrid steepest descent methods for variational inequalities in Banach spaces”, Num. Funct. Anal. Optim., 29:9–10 (2008), 987–1033 | DOI | MR

[8] Xu H. K., “An iterative approach to quadratic optimization”, J. Optim. Theory Appl., 116 (2003), 659–678 | DOI | MR | Zbl

[9] Suzuki T., “Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces”, Proc. Amer. Math. Soc., 135 (2007), 99–106 | DOI | MR | Zbl