Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2021; 58(3): 525-552

Online first article April 5, 2021      Printed May 1, 2021

https://doi.org/10.4134/JKMS.j180808

Copyright © The Korean Mathematical Society.

General iterative algorithms for monotone inclusion, variational inequality and fixed point problems

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)