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A new general system of variational inequalities for convergence theorem and application

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Abstract

In this present paper, we propose a modified form of generalized system of variational inequalities and introduce an iterative scheme for finding a common element of the set of fixed points of nonexpansive mapping and the solution set of the proposed problem in the framework of real Hilbert spaces. We prove a strong convergence theorem of the proposed iterative scheme. Applying our main result, we prove strong convergence theorems of the standard constrained convex optimization problem and the split feasibility problem. In support of our main result, a numerical example is also presented.

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Funding

This research was supported by Research and Innovation Services of King Mongkut’s Institute of Tecnology Ladkrabang.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, 10520, Thailand

    Keerati Siriyan & Atid Kangtunyakarn

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  1. Keerati Siriyan
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  2. Atid Kangtunyakarn
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Correspondence to Atid Kangtunyakarn.

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Siriyan, K., Kangtunyakarn, A. A new general system of variational inequalities for convergence theorem and application. Numer Algor 81, 99–123 (2019). https://doi.org/10.1007/s11075-018-0537-8

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  • DOI: https://doi.org/10.1007/s11075-018-0537-8

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