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Relaxed and Hybrid Viscosity Methods for General System of Variational Inequalities with Split Feasibility Problem Constrain

DOI: 10.1186/1687-1812-2013-43

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Abstract:

In this paper, we propose and analyze some relaxed and hybrid viscosity iterative algorithms for finding a common element of the solution set $\it\Xi$ of a general system of variational inequalities, the solution set $\it\Gamma$ of a split feasibility problem and the fixed point set ${\rm Fix}(S)$ of a strictly pseudocontractive mapping $S$ in the setting of infinite-dimensional Hilbert spaces. We prove that the sequences generated by the proposed algorithms converge strongly to an element of ${\rm Fix}(S)\cap{\it\Xi}\cap{\it\Gamma}$ under mild conditions..

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