Mebawondu, Akindele, Pillay, Paranjothi, Narain, Ojen, Onifade, Akindele, Adewole, Mathew. (1401). Some iterative algorithms for Reich-Suzuki nonexpansive mappings and relaxed $(\alpha,k)$-cocoercive mapping with applications to a fixed point and optimization problems. هنرهای کاربردی, 14(2), 175-193. doi: 10.22075/ijnaa.2022.27076.3489
Akindele Adebayo Mebawondu; Paranjothi Pillay; Ojen K. Narain; Akindele Akano Onifade; Mathew O. Adewole. "Some iterative algorithms for Reich-Suzuki nonexpansive mappings and relaxed $(\alpha,k)$-cocoercive mapping with applications to a fixed point and optimization problems". هنرهای کاربردی, 14, 2, 1401, 175-193. doi: 10.22075/ijnaa.2022.27076.3489
Mebawondu, Akindele, Pillay, Paranjothi, Narain, Ojen, Onifade, Akindele, Adewole, Mathew. (1401). 'Some iterative algorithms for Reich-Suzuki nonexpansive mappings and relaxed $(\alpha,k)$-cocoercive mapping with applications to a fixed point and optimization problems', هنرهای کاربردی, 14(2), pp. 175-193. doi: 10.22075/ijnaa.2022.27076.3489
Mebawondu, Akindele, Pillay, Paranjothi, Narain, Ojen, Onifade, Akindele, Adewole, Mathew. Some iterative algorithms for Reich-Suzuki nonexpansive mappings and relaxed $(\alpha,k)$-cocoercive mapping with applications to a fixed point and optimization problems. هنرهای کاربردی, 1401; 14(2): 175-193. doi: 10.22075/ijnaa.2022.27076.3489

Some iterative algorithms for Reich-Suzuki nonexpansive mappings and relaxed $(\alpha,k)$-cocoercive mapping with applications to a fixed point and optimization problems

International Journal of Nonlinear Analysis and Applications
مقاله 16، دوره 14، شماره 2، اردیبهشت 2023، صفحه 175-193    اصل مقاله (548.54 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.27076.3489
نویسندگان
Akindele Adebayo Mebawondu* 1، 2؛ Paranjothi Pillay1؛ Ojen K. Narain1؛ Akindele Akano Onifade3؛ Mathew O. Adewole3
1School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa
2DST-NRF Center of Excellence in Mathematical and Statistical Sciences (CoE-MaSS)
3Department of Computer Science and Mathematics, Mountain Top University, Prayer City, Ogun State, Nigeria
چکیده
In this paper, we propose an iterative method for finding the common element of the set of fixed points of Reich-Suzuki nonexpansive mappings and the set of solutions of the variational inequalities problems in the framework of Hilbert spaces. In addition, we establish convergence results for these proposed iterative methods under some mild conditions. Furthermore, we establish analytically and numerically that our newly proposed iterative method converges to a common element of the set of fixed points of a Reich-Suzuki nonexpansive mapping and the set of solutions of the variational inequalities problems faster compared to some well-known iterative methods in the literature. Finally, we apply our proposed iterative method to approximate the solution of a convex minimization problem. The results obtained in this paper improve, extend and unify some related results in the literature.
کلیدواژه‌ها
Variational inequality problem؛ inertial iterative scheme؛ fixed point problem؛ Reich-Suzuki nonexpansive mappings
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