2014
DOI: 10.1186/1687-1812-2014-11
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Weak- and strong-convergence theorems of solutions to split feasibility problem for nonspreading type mapping in Hilbert spaces

Abstract: The purpose of this article is to study the weak-and strong-convergence theorems of solutions to split a feasibility problem for a family of nonspreading-type mapping in Hilbert spaces. The main result presented in this paper improves and extends some recent results of Censor et al., Byrne, Yang, Moudafi, Xu, Censor and Segal, Masad and Reich, and others. As an application, we solve the hierarchical variational inequality problem by using the main theorem. MSC: 47J05; 47H09; 49J25

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Cited by 17 publications
(13 citation statements)
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“…The original (unknown) image x † is known a priori to belong D; given only the metric projections P C i recover x † by an iterative scheme. This problem is referred to as the convex feasibility problem (CFP), see for instance [1,4,5,7,10,18]. One effective approach for solving (CFP) is algorithmic iteration.…”
Section: Problem Statementmentioning
confidence: 99%
“…The original (unknown) image x † is known a priori to belong D; given only the metric projections P C i recover x † by an iterative scheme. This problem is referred to as the convex feasibility problem (CFP), see for instance [1,4,5,7,10,18]. One effective approach for solving (CFP) is algorithmic iteration.…”
Section: Problem Statementmentioning
confidence: 99%
“…2 Department of Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang, 050003, China. 3 The Second Training Base, Naval Aviation Institution, Huludao, 125001, China.…”
Section: Numerical Experimentsmentioning
confidence: 99%
“…In [10], Moudafi proposed an iteration scheme and obtained a weak convergence theorem of the split common fixed point problem for demicontractive mappings in the setting of two Hilbert spaces. Since then, the split common fixed point problems of other nonlinear mappings in the setting of two Hilbert spaces have been studied by some authors, see, for instance, [7,8,10,11,13,14,20].…”
Section: Introductionmentioning
confidence: 99%