کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
843960 908571 2009 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Viscosity approximation methods for countable families of nonexpansive mappings in Banach spaces
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی (عمومی)
پیش نمایش صفحه اول مقاله
Viscosity approximation methods for countable families of nonexpansive mappings in Banach spaces
چکیده انگلیسی

Let CC be a nonempty closed convex subset of a Banach space EE and let {Sn}{Sn} be a family of nonexpansive mappings of CC into itself such that the set of common fixed points of {Sn}{Sn} is nonempty. We first introduce a sequence {xn}{xn} of CC defined by x1=x∈Cx1=x∈C and xn+1=αnf(xn)+(1−αn)Snxnfor alln∈N, where {αn}⊂(0,1){αn}⊂(0,1) and ff is a contraction of CC into itself. Further, we give the conditions of {αn}{αn} and {Sn}{Sn} under which {xn}{xn} converges strongly to a common fixed point of {Sn}{Sn}. This result generalizes the strong convergence theorem for nonexpansive mappings by Suzuki [T. Suzuki, A sufficient and necessary condition for Halpern-type strong convergence to fixed points of nonexpansive mappings, Proc. Amer. Math. Soc. 135 (2007) 99–106] and the strong convergence theorem for accretive operators by Kamimura and Takahashi [S. Kamimura, W. Takahashi, Weak and strong convergence of solutions to accretive operator inclusions and applications, Set-Valued Anal. 8 (2000) 361–374], simultaneously. Using this result, we improve and extend the two above-mentioned results.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 70, Issue 2, 15 January 2009, Pages 719–734
نویسندگان
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