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:: Volume 6, Issue 3 (Vol. 6, No. 3 2020) ::
Mathematical Researches 2020, 6(3): 0-0 Back to browse issues page
Strong convergence of variational inequality problem Over the set of common fixed points of a family of demi-contractive mappings
Mohammad Eslamian Dr
University of Science and Technology of Mazandaran , mhmdeslamian@gmail.com
Abstract:   (450 Views)
In this paper, by using the viscosity iterative method and the hybrid steepest-descent method, we present a new algorithm for solving the variational inequality problem. The sequence generated by this algorithm is strong convergence to a common element of the set of common zero points of a finite family of inverse strongly monotone operators and the set of common fixed points of a finite family of demi-contractive mappings. Also, we prove that the sequence generated by this algorithm is strong convergence to a solution of a system of variational inequalities over the set of common fixed points of quasi-nonexpansive mappings and strict pseudo-contractive mappings in a Hilbert space. Finally, some applications of this results are present for solving the split common fixed point problem, which entails finding a point which belongs to the set of common fixed points of a finite family of of strict pseudo-contractive mappings in a Hilbert space such that its image under a linear transformation belongs to the set of common fixed points of a finite family of nonexpasive mappings in the image space.
Keywords: Variational inequality problem, demi-contractive mappings, fixed point, strict pseudo-contractive mappings
     
Type of Study: Original Manuscript | Subject: alg
Received: 2018/03/26 | Accepted: 2019/01/26 | Published: 2020/11/30 | ePublished: 2020/11/30
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Eslamian M. Strong convergence of variational inequality problem Over the set of common fixed points of a family of demi-contractive mappings. Mathematical Researches. 2020; 6 (3)
URL: http://mmr.khu.ac.ir/article-1-2763-en.html


Volume 6, Issue 3 (Vol. 6, No. 3 2020) Back to browse issues page
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