A Strong Convergence Theorem for Split Null Point Problem and Generalized Mixed Equilibrium Problem in Real Hilbert Spaces
In this paper, we study a schematic approximation of solutions of a split null point problem for a finite family of maximal monotone operators in real Hilbert spaces. We propose an iterative algorithm that does not depend on the operator norm which solves the split null point problem and also solves...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-02-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/10/1/16 |
| _version_ | 1797414645735096320 |
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| author | Olawale Kazeem Oyewole Oluwatosin Temitope Mewomo |
| author_facet | Olawale Kazeem Oyewole Oluwatosin Temitope Mewomo |
| author_sort | Olawale Kazeem Oyewole |
| collection | DOAJ |
| description | In this paper, we study a schematic approximation of solutions of a split null point problem for a finite family of maximal monotone operators in real Hilbert spaces. We propose an iterative algorithm that does not depend on the operator norm which solves the split null point problem and also solves a generalized mixed equilibrium problem. We prove a strong convergence of the proposed algorithm to a common solution of the two problems. We display some numerical examples to illustrate our method. Our result improves some existing results in the literature. |
| first_indexed | 2024-03-09T05:36:25Z |
| format | Article |
| id | doaj.art-37f82ad8a5de4bf4a3d33322fe687a64 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T05:36:25Z |
| publishDate | 2021-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-37f82ad8a5de4bf4a3d33322fe687a642023-12-03T12:28:21ZengMDPI AGAxioms2075-16802021-02-011011610.3390/axioms10010016A Strong Convergence Theorem for Split Null Point Problem and Generalized Mixed Equilibrium Problem in Real Hilbert SpacesOlawale Kazeem Oyewole0Oluwatosin Temitope Mewomo1School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4001, South AfricaSchool of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4001, South AfricaIn this paper, we study a schematic approximation of solutions of a split null point problem for a finite family of maximal monotone operators in real Hilbert spaces. We propose an iterative algorithm that does not depend on the operator norm which solves the split null point problem and also solves a generalized mixed equilibrium problem. We prove a strong convergence of the proposed algorithm to a common solution of the two problems. We display some numerical examples to illustrate our method. Our result improves some existing results in the literature.https://www.mdpi.com/2075-1680/10/1/16split feasibility problemnull point problemgeneralized mixed equilibrium problemmonotone mappingstrong convergenceHilbert space |
| spellingShingle | Olawale Kazeem Oyewole Oluwatosin Temitope Mewomo A Strong Convergence Theorem for Split Null Point Problem and Generalized Mixed Equilibrium Problem in Real Hilbert Spaces Axioms split feasibility problem null point problem generalized mixed equilibrium problem monotone mapping strong convergence Hilbert space |
| title | A Strong Convergence Theorem for Split Null Point Problem and Generalized Mixed Equilibrium Problem in Real Hilbert Spaces |
| title_full | A Strong Convergence Theorem for Split Null Point Problem and Generalized Mixed Equilibrium Problem in Real Hilbert Spaces |
| title_fullStr | A Strong Convergence Theorem for Split Null Point Problem and Generalized Mixed Equilibrium Problem in Real Hilbert Spaces |
| title_full_unstemmed | A Strong Convergence Theorem for Split Null Point Problem and Generalized Mixed Equilibrium Problem in Real Hilbert Spaces |
| title_short | A Strong Convergence Theorem for Split Null Point Problem and Generalized Mixed Equilibrium Problem in Real Hilbert Spaces |
| title_sort | strong convergence theorem for split null point problem and generalized mixed equilibrium problem in real hilbert spaces |
| topic | split feasibility problem null point problem generalized mixed equilibrium problem monotone mapping strong convergence Hilbert space |
| url | https://www.mdpi.com/2075-1680/10/1/16 |
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