Abstract
In this article, we prove some properties of a demicontractive mapping defined on a nonempty closed convex subset of a Hilbert space. By using these properties, we obtain strong convergence theorems of a hybrid shrinking projection method for finding a common element of the set of common fixed points of a finite family of demicontractive mappings and the set of common solutions of a finite family of variational inequality problems in a Hilbert space. A numerical example is presented to illustrate the proposed method and convergence result. Our results improve and extend the corresponding results existing in the literature.
Citation
Suthep Suantai. Withun Phuengrattana. "A hybrid shrinking projection method for common fixed points of a finite family of demicontractive mappings with variational inequality problems." Banach J. Math. Anal. 11 (3) 661 - 675, July 2017. https://doi.org/10.1215/17358787-2017-0010
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