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System of Extended General Variational Inequalities for Relaxed Cocoercive Mappings in Hilbert Space

Graduate School of Education, Kyungnam University, Changwon 51767, Gyeongnam, Korea
Mathematics 2018, 6(10), 198; https://doi.org/10.3390/math6100198
Received: 7 September 2018 / Revised: 4 October 2018 / Accepted: 9 October 2018 / Published: 11 October 2018
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Abstract

In this manuscript, we study a system of extended general variational inequalities (SEGVI) with several nonlinear operators, more precisely, six relaxed ( α , r ) -cocoercive mappings. Using the projection method, we show that a system of extended general variational inequalities is equivalent to the nonlinear projection equations. This alternative equivalent problem is used to consider the existence and convergence (or approximate solvability) of a solution of a system of extended general variational inequalities under suitable conditions. View Full-Text
Keywords: a system of extended general variational inequality (SEGVI); auxiliary system of extended general variational inequality; relaxed (α,r)-cocoercive mapping; projection method; solution; fixed point a system of extended general variational inequality (SEGVI); auxiliary system of extended general variational inequality; relaxed (α,r)-cocoercive mapping; projection method; solution; fixed point
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Kim, K.S. System of Extended General Variational Inequalities for Relaxed Cocoercive Mappings in Hilbert Space. Mathematics 2018, 6, 198.

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