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

Kyung Soo Kim
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Kyung Soo Kim: Graduate School of Education, Kyungnam University, Changwon 51767, Gyeongnam, Korea

Mathematics, 2018, vol. 6, issue 10, 1-12

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.

Keywords: a system of extended general variational inequality (SEGVI); auxiliary system of extended general variational inequality; relaxed ( ? , r )-cocoercive mapping; projection method; solution; fixed point (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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