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Existence and algorithm of solutions for general set-valued Noor variational inequalities with relaxed (μ,ν)-cocoercive operators in Hilbert spaces

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Abstract

The purpose of this paper is to suggest and analyze a number of iterative algorithms for solving the generalized set-valued variational inequalities in the sense of Noor in Hilbert spaces. Moreover, we show some relationships between the generalized set-valued variational inequality problem in the sense of Noor and the generalized set-valued Wiener-Hopf equations involving continuous operator. Consequently, by using the equivalence, we also establish some methods for finding the solutions of generalized set-valued Wiener-Hopf equations involving continuous operator. Our results can be viewed as a refinement and improvement of the previously known results for variational inequality theory.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000, Thailand

    Narin Petrot

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  1. Narin Petrot
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Correspondence to Narin Petrot.

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This work was supported by The Thailand Research Fund (Project No. MRG5180178) and Faculty of Science, Naresuan University, Thailand.

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Petrot, N. Existence and algorithm of solutions for general set-valued Noor variational inequalities with relaxed (μ,ν)-cocoercive operators in Hilbert spaces. J. Appl. Math. Comput. 32, 393–404 (2010). https://doi.org/10.1007/s12190-009-0258-1

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  • DOI: https://doi.org/10.1007/s12190-009-0258-1

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