A Generalized Explicit Iterative Method for Solving Generalized Split Feasibility Problem and Fixed Point Problem in Real Banach Spaces
In this paper, we propose a generalized explicit algorithm for approximating the common solution of generalized split feasibility problem and the fixed point of demigeneralized mapping in uniformly smooth and 2-uniformly convex real Banach spaces. The generalized split feasibility problem is a gener...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-02-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/2/335 |
| _version_ | 1797476405824454656 |
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| author | Godwin Chidi Ugwunnadi Lateef Olakunle Jolaoso Chibueze Christian Okeke |
| author_facet | Godwin Chidi Ugwunnadi Lateef Olakunle Jolaoso Chibueze Christian Okeke |
| author_sort | Godwin Chidi Ugwunnadi |
| collection | DOAJ |
| description | In this paper, we propose a generalized explicit algorithm for approximating the common solution of generalized split feasibility problem and the fixed point of demigeneralized mapping in uniformly smooth and 2-uniformly convex real Banach spaces. The generalized split feasibility problem is a general mathematical problem in the sense that it unifies several mathematical models arising in (symmetry and non-symmetry) optimization theory and also finds many applications in applied science. We designed the algorithm in such a way that the convergence analysis does not need a prior estimate of the operator norm. More so, we establish the strong convergence of our algorithm and present some computational examples to illustrate the performance of the proposed method. In addition, we give an application of our result for solving the image restoration problem and compare with other algorithms in the literature. This result improves and generalizes many important related results in the contemporary literature. |
| first_indexed | 2024-03-09T20:57:19Z |
| format | Article |
| id | doaj.art-5083f34f45fc458f8aeda1db1695d347 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T20:57:19Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-5083f34f45fc458f8aeda1db1695d3472023-11-23T22:16:56ZengMDPI AGSymmetry2073-89942022-02-0114233510.3390/sym14020335A Generalized Explicit Iterative Method for Solving Generalized Split Feasibility Problem and Fixed Point Problem in Real Banach SpacesGodwin Chidi Ugwunnadi0Lateef Olakunle Jolaoso1Chibueze Christian Okeke2Department of Mathematics, University of Eswatini, Private Bag 4, Kwaluseni M201, EswatiniDepartment of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 94, Medunsa 0204, South AfricaSchool of Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South AfricaIn this paper, we propose a generalized explicit algorithm for approximating the common solution of generalized split feasibility problem and the fixed point of demigeneralized mapping in uniformly smooth and 2-uniformly convex real Banach spaces. The generalized split feasibility problem is a general mathematical problem in the sense that it unifies several mathematical models arising in (symmetry and non-symmetry) optimization theory and also finds many applications in applied science. We designed the algorithm in such a way that the convergence analysis does not need a prior estimate of the operator norm. More so, we establish the strong convergence of our algorithm and present some computational examples to illustrate the performance of the proposed method. In addition, we give an application of our result for solving the image restoration problem and compare with other algorithms in the literature. This result improves and generalizes many important related results in the contemporary literature.https://www.mdpi.com/2073-8994/14/2/335demigeneralized mappingfixed pointmonotone mappingmid-point methodstrong convergenceBanach spaces |
| spellingShingle | Godwin Chidi Ugwunnadi Lateef Olakunle Jolaoso Chibueze Christian Okeke A Generalized Explicit Iterative Method for Solving Generalized Split Feasibility Problem and Fixed Point Problem in Real Banach Spaces Symmetry demigeneralized mapping fixed point monotone mapping mid-point method strong convergence Banach spaces |
| title | A Generalized Explicit Iterative Method for Solving Generalized Split Feasibility Problem and Fixed Point Problem in Real Banach Spaces |
| title_full | A Generalized Explicit Iterative Method for Solving Generalized Split Feasibility Problem and Fixed Point Problem in Real Banach Spaces |
| title_fullStr | A Generalized Explicit Iterative Method for Solving Generalized Split Feasibility Problem and Fixed Point Problem in Real Banach Spaces |
| title_full_unstemmed | A Generalized Explicit Iterative Method for Solving Generalized Split Feasibility Problem and Fixed Point Problem in Real Banach Spaces |
| title_short | A Generalized Explicit Iterative Method for Solving Generalized Split Feasibility Problem and Fixed Point Problem in Real Banach Spaces |
| title_sort | generalized explicit iterative method for solving generalized split feasibility problem and fixed point problem in real banach spaces |
| topic | demigeneralized mapping fixed point monotone mapping mid-point method strong convergence Banach spaces |
| url | https://www.mdpi.com/2073-8994/14/2/335 |
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