On synchronal algorithm for fixed point and variational inequality problems in hilbert spaces

L M Bulama; A Kılıçman

doi:10.1186/s40064-016-1723-6

On synchronal algorithm for fixed point and variational inequality problems in hilbert spaces

Springerplus. 2016 Feb 1:5:103. doi: 10.1186/s40064-016-1723-6. eCollection 2016.

Authors

L M Bulama¹, A Kılıçman¹

Affiliation

¹ Department of Mathematics, Universiti Putra Malaysia (UPM), 43400 Serdang, Selangor Malaysia.

Abstract

The aim of this article is to expand and generalize some approximation methods proposed by Tian and Di (J Fixed Point Appl, 2011. doi:10.1186/1687-1812-21) to the class of [Formula: see text]-total asymptotically strict pseudocontraction to solve the fixed point problem as well as variational inequality problem in the frame work of Hilbert space. Further, the results presented in this paper extend, improve and also generalize several known results in the literature .

Keywords: Fixed point and variational inequality problem; K-strict pseudo-contraction; Nonexpansive mapping; Synchronal algorithm; Total strict asymptotically pseudocontraction.