Journal Article10.1007/S11590-013-0629-2
An iterative method for split variational inclusion problem and fixed point problem for a nonexpansive mapping
K.R. Kazmi,S. H. Rizvi +1 more
136
TL;DR: It is proved that the sequences generated by the proposed iterative method converge strongly to a common solution of split variational inclusion problem and fixed point problem for a nonexpansive mapping which is the unique solution of the variational inequality problem.
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Abstract: In this paper, we introduce and study an iterative method to approximate a common solution of split variational inclusion problem and fixed point problem for a nonexpansive mapping in real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of split variational inclusion problem and fixed point problem for a nonexpansive mapping which is the unique solution of the variational inequality problem. The results presented in this paper are the supplement, extension and generalization of the previously known results in this area.
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Citations
An iterative method for solving split monotone variational inclusion and fixed point problems
Yekini Shehu,F. U. Ogbuisi +1 more
TL;DR: In this paper, an iterative algorithm for finding an approximate solution of a split monotone variational inclusion problem with fixed point problem for strictly pseudocontractive maps in real Hilbert spaces is proposed.
51
On a system of monotone variational inclusion problems with fixed-point constraint
TL;DR: In this article , a new iterative method that employs an inertial technique with self-adaptive step size for approximating the solution of the monotone variational inclusion problem in Hilbert spaces was proposed.
A hybrid viscosity algorithm via modify the hybrid steepest descent method for solving the split variational inclusion in image reconstruction and fixed point problems
TL;DR: A new viscosity approximation method is introduced by modify the hybrid steepest descent method for finding a common solution of split variational inclusion problem and fixed point problem of a countable family of nonexpansive mappings and it is proved that the sequences generated by the proposed iterative method converge strongly to acommon solution.
48
Strong Convergence of Self-adaptive Inertial Algorithms for Solving Split Variational Inclusion Problems with Applications
TL;DR: In this paper, four self-adaptive iterative iterative algorithms with inertial effects are introduced to solve a split variational inclusion problem in real Hilbert spaces, and strong convergence theorems of these algorithms are established under mild and standard assumptions.
43
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