General iterative algorithms for monotone inclusion, variational inequality and fixed point problems
J. Korean Math. Soc. 2021 Vol. 58, No. 3, 525-552
https://doi.org/10.4134/JKMS.j180808
Published online April 5, 2021
Printed May 1, 2021
Jong Soo Jung
Dong-A University
Abstract : In this paper, we introduce two general iterative algorithms (one implicit algorithm and one explicit algorithm) for finding a common element of the solution set of the variational inequality problems for a continuous monotone mapping, the zero point set of a set-valued maximal monotone operator, and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. Then we establish strong convergence of the proposed iterative algorithms to a common point of three sets, which is a solution of a certain variational inequality. Further, we find the minimum-norm element in common set of three sets.
Keywords : Maximal monotone operator, variational inequality, zeros, fixed points, continuous monotone mapping, continuous pseudocontractive mapping, minimum-norm point
MSC numbers : 47H05, 47H09, 47H10, 47J05, 47J20, 47J25
Supported by : This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2018R1D1A1B07045718)
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