Soori, Ebrahim, Agarwal, Ravi, ORegan, Donal. (1400). A Simple proof for the algorithms of relaxed $(u, v)$-cocoercive mappings and $\alpha$-inverse strongly monotone mappings. هنرهای کاربردی, 12(2), 327-333. doi: 10.22075/ijnaa.2019.18336.2004
Ebrahim Soori; Ravi Agarwal; Donal ORegan. "A Simple proof for the algorithms of relaxed $(u, v)$-cocoercive mappings and $\alpha$-inverse strongly monotone mappings". هنرهای کاربردی, 12, 2, 1400, 327-333. doi: 10.22075/ijnaa.2019.18336.2004
Soori, Ebrahim, Agarwal, Ravi, ORegan, Donal. (1400). 'A Simple proof for the algorithms of relaxed $(u, v)$-cocoercive mappings and $\alpha$-inverse strongly monotone mappings', هنرهای کاربردی, 12(2), pp. 327-333. doi: 10.22075/ijnaa.2019.18336.2004
Soori, Ebrahim, Agarwal, Ravi, ORegan, Donal. A Simple proof for the algorithms of relaxed $(u, v)$-cocoercive mappings and $\alpha$-inverse strongly monotone mappings. هنرهای کاربردی, 1400; 12(2): 327-333. doi: 10.22075/ijnaa.2019.18336.2004

A Simple proof for the algorithms of relaxed $(u, v)$-cocoercive mappings and $\alpha$-inverse strongly monotone mappings

International Journal of Nonlinear Analysis and Applications
دوره 12، شماره 2، بهمن 2021، صفحه 327-333    اصل مقاله (393.41 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2019.18336.2004
نویسندگان
Ebrahim Soori* 1؛ Ravi Agarwal2؛ Donal ORegan3
1Department of Mathematics, Lorestan University, P.O. Box 465, Khoramabad, Lorestan, Iran
2Department of Mathematics Texas and University-Kingsville 700 University Blvd., MSC 172 Kingsville, Texas 78363-8202, USA
3School of Mathematics, Statistics, National University of Ireland, Galway, Ireland
چکیده
In this paper, a simple proof is presented for the convergence of the algorithms for the class of relaxed $(u, v)$-cocoercive mappings and $\alpha$-inverse strongly monotone mappings. Based on $\alpha$-expansive maps, for example, a simple proof of the convergence of the recent iterative algorithms by relaxed $(u, v)$-cocoercive mappings due to Kumam-Jaiboon is provided. Also a simple proof for the convergence of the iterative algorithms by inverse-strongly monotone mappings due to Iiduka-Takahashi in a special case is provided. These results are an improvement as well as a refinement of previously known results.
کلیدواژه‌ها
Inverse-strongly monotone mapping؛ Strongly monotone mapping؛ Relaxed $(u, v)$-cocoercive mapping
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