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Saeidi, S.. (1388). Comments on relaxed $(\gamma, r)$-cocoercive mappings. هنرهای کاربردی, 1(1), 54-57. doi: 10.22075/ijnaa.2010.68
S. Saeidi. "Comments on relaxed $(\gamma, r)$-cocoercive mappings". هنرهای کاربردی, 1, 1, 1388, 54-57. doi: 10.22075/ijnaa.2010.68
Saeidi, S.. (1388). 'Comments on relaxed $(\gamma, r)$-cocoercive mappings', هنرهای کاربردی, 1(1), pp. 54-57. doi: 10.22075/ijnaa.2010.68
Saeidi, S.. Comments on relaxed $(\gamma, r)$-cocoercive mappings. هنرهای کاربردی, 1388; 1(1): 54-57. doi: 10.22075/ijnaa.2010.68

Comments on relaxed $(\gamma, r)$-cocoercive mappings

International Journal of Nonlinear Analysis and Applications
مقاله 6، دوره 1، شماره 1، فروردین 2010، صفحه 54-57    اصل مقاله (136.48 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2010.68
نویسنده
S. Saeidi*
Department of Mathematics, University of Kurdistan, Sanandaj 416, Kurdistan, Iran.
تاریخ دریافت: 31 فروردین 1388،  تاریخ بازنگری: 14 آبان 1388،  تاریخ پذیرش: 24 آبان 1388 
چکیده
We show that the variational inequality $VI(C,A)$ has a unique solution for a relaxed $(\gamma , r)$-cocoercive, $\mu$-Lipschitzian mapping $A: Cto H$ with $r>\gamma \mu^2$, where $C$ is a nonempty closed convex subset of a Hilbert space $H$. From this result, it can be derived that, for example, the recent algorithms given in the references of this paper, despite their becoming more complicated, are not general as they should be.
کلیدواژه‌ها
Common element؛ Contraction؛ Fixed point؛ Iteration؛ Nonexpansive mapping؛ Relaxed $(gamma , r)$-cocoercive mappings؛ variational inequality
مراجع
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