Displaying similar documents to “Convergence theorems on an iterative method for variational inequality problems and fixed point problems.”

Strong convergence of an iterative method for variational inequality problems and fixed point problems

Xiao Long Qin, Shin Min Kang, Yong Fu Su, Mei Juan Shang (2009)

Archivum Mathematicum

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In this paper, we introduce a general iterative scheme to investigate the problem of finding a common element of the fixed point set of a strict pseudocontraction and the solution set of a variational inequality problem for a relaxed cocoercive mapping by viscosity approximate methods. Strong convergence theorems are established in a real Hilbert space.

An extragradient approximation method for variational inequality problem on fixed point problem of nonexpensive mappings and monotone mappings

Alongkot Suvarnamani, Mongkol Tatong (2012)

Archivum Mathematicum

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We introduce an iterative sequence for finding the common element of the set of fixed points of a nonexpansive mapping and the solutions of the variational inequality problem for tree inverse-strongly monotone mappings. Under suitable conditions, some strong convergence theorems for approximating a common element of the above two sets are obtained. Moreover, using the above theorem, we also apply to finding solutions of a general system of variational inequality and a zero of a maximal...