An Iterative Method for Solving Split Monotone Variational Inclusion Problems and Finite Family of Variational Inequality Problems in Hilbert Spaces
The purpose of this paper is to study the convergence analysis of an intermixed algorithm for finding the common element of the set of solutions of split monotone variational inclusion problem (SMIV) and the set of a finite family of variational inequality problems. Under the suitable assumption, a...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2021/4273851 |
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| author | Wanna Sriprad Somnuk Srisawat |
| author_facet | Wanna Sriprad Somnuk Srisawat |
| author_sort | Wanna Sriprad |
| collection | DOAJ |
| description | The purpose of this paper is to study the convergence analysis of an intermixed algorithm for finding the common element of the set of solutions of split monotone variational inclusion problem (SMIV) and the set of a finite family of variational inequality problems. Under the suitable assumption, a strong convergence theorem has been proved in the framework of a real Hilbert space. In addition, by using our result, we obtain some additional results involving split convex minimization problems (SCMPs) and split feasibility problems (SFPs). Also, we give some numerical examples for supporting our main theorem. |
| format | Article |
| id | doaj-art-1b0f4d6706ee4dddabe4d76fe21b1448 |
| institution | Kabale University |
| issn | 1687-0425 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1b0f4d6706ee4dddabe4d76fe21b14482025-02-03T05:59:57ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252021-01-01202110.1155/2021/4273851An Iterative Method for Solving Split Monotone Variational Inclusion Problems and Finite Family of Variational Inequality Problems in Hilbert SpacesWanna Sriprad0Somnuk Srisawat1Department of Mathematics and Computer ScienceDepartment of Mathematics and Computer ScienceThe purpose of this paper is to study the convergence analysis of an intermixed algorithm for finding the common element of the set of solutions of split monotone variational inclusion problem (SMIV) and the set of a finite family of variational inequality problems. Under the suitable assumption, a strong convergence theorem has been proved in the framework of a real Hilbert space. In addition, by using our result, we obtain some additional results involving split convex minimization problems (SCMPs) and split feasibility problems (SFPs). Also, we give some numerical examples for supporting our main theorem.http://dx.doi.org/10.1155/2021/4273851 |
| spellingShingle | Wanna Sriprad Somnuk Srisawat An Iterative Method for Solving Split Monotone Variational Inclusion Problems and Finite Family of Variational Inequality Problems in Hilbert Spaces International Journal of Mathematics and Mathematical Sciences |
| title | An Iterative Method for Solving Split Monotone Variational Inclusion Problems and Finite Family of Variational Inequality Problems in Hilbert Spaces |
| title_full | An Iterative Method for Solving Split Monotone Variational Inclusion Problems and Finite Family of Variational Inequality Problems in Hilbert Spaces |
| title_fullStr | An Iterative Method for Solving Split Monotone Variational Inclusion Problems and Finite Family of Variational Inequality Problems in Hilbert Spaces |
| title_full_unstemmed | An Iterative Method for Solving Split Monotone Variational Inclusion Problems and Finite Family of Variational Inequality Problems in Hilbert Spaces |
| title_short | An Iterative Method for Solving Split Monotone Variational Inclusion Problems and Finite Family of Variational Inequality Problems in Hilbert Spaces |
| title_sort | iterative method for solving split monotone variational inclusion problems and finite family of variational inequality problems in hilbert spaces |
| url | http://dx.doi.org/10.1155/2021/4273851 |
| work_keys_str_mv | AT wannasriprad aniterativemethodforsolvingsplitmonotonevariationalinclusionproblemsandfinitefamilyofvariationalinequalityproblemsinhilbertspaces AT somnuksrisawat aniterativemethodforsolvingsplitmonotonevariationalinclusionproblemsandfinitefamilyofvariationalinequalityproblemsinhilbertspaces AT wannasriprad iterativemethodforsolvingsplitmonotonevariationalinclusionproblemsandfinitefamilyofvariationalinequalityproblemsinhilbertspaces AT somnuksrisawat iterativemethodforsolvingsplitmonotonevariationalinclusionproblemsandfinitefamilyofvariationalinequalityproblemsinhilbertspaces |