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Open AccessArticle

A Parallel-Viscosity-Type Subgradient Extragradient-Line Method for Finding the Common Solution of Variational Inequality Problems Applied to Image Restoration Problems

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Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
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School of Science, University of Phayao, Phayao 56000, Thailand
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Author to whom correspondence should be addressed.
Mathematics 2020, 8(2), 248; https://doi.org/10.3390/math8020248
Received: 8 January 2020 / Revised: 7 February 2020 / Accepted: 9 February 2020 / Published: 14 February 2020
In this paper, we study a modified viscosity type subgradient extragradient-line method with a parallel monotone hybrid algorithm for approximating a common solution of variational inequality problems. Under suitable conditions in Hilbert spaces, the strong convergence theorem of the proposed algorithm to such a common solution is proved. We then give numerical examples in both finite and infinite dimensional spaces to justify our main theorem. Finally, we can show that our proposed algorithm is flexible and has good quality for use with common types of blur effects in image recovery.
Keywords: variational inequality problems; viscosity-type subgradient extragradient-line method; monotone mapping; Hilbert space variational inequality problems; viscosity-type subgradient extragradient-line method; monotone mapping; Hilbert space
MDPI and ACS Style

Suantai, S.; Peeyada, P.; Yambangwai, D.; Cholamjiak, W. A Parallel-Viscosity-Type Subgradient Extragradient-Line Method for Finding the Common Solution of Variational Inequality Problems Applied to Image Restoration Problems. Mathematics 2020, 8, 248.

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