کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
842687 908537 2010 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
An explicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of an infinite family of nonexpansive mappings
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی (عمومی)
پیش نمایش صفحه اول مقاله
An explicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of an infinite family of nonexpansive mappings
چکیده انگلیسی

Let HH be a Hilbert space and CC be a nonempty closed convex subset of HH, {Ti}i∈N{Ti}i∈N be a family of nonexpansive mappings from CC into HH, Gi:C×C→RGi:C×C→R be a finite family of equilibrium functions (i∈{1,2,…,K})(i∈{1,2,…,K}), AA be a strongly positive bounded linear operator with a coefficient γ̄ and Bλ-Lipschitzian, relaxed (μ,ν)(μ,ν)-cocoercive map of CC into HH. Moreover, let {rk,n}k=1K, {αn}{αn} satisfy appropriate conditions and F≔(∩k=1KEP(Gk))∩VI(C,B)∩(∩n∈NFix(Tn))≠0̸; we introduce an explicit scheme which defines a suitable sequence as follows: xn+1=αnγf(xn)+(1−αnA)WnPC(I−snB)Sr1,n1Sr2,n2⋯SrK,nKxn∀n∈N and {xn}{xn} strongly converges to x∗∈Fx∗∈F which satisfies the variational inequality 〈(A−γf)x∗,x−x∗〉≥0〈(A−γf)x∗,x−x∗〉≥0 for all x∈Fx∈F. The results presented in this paper mainly extend and improve a recent result of Colao [V. Colao, An implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings, Nonlinear Analysis (2009), http://dx.doi.org/10.1016/j.na.2009.01.115] and Qin [X. Qin, M. Shang, Y. Su, A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces, Nonlinear Analysis 69 (2008) 3897–3909].

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 72, Issue 6, 15 March 2010, Pages 3124–3135
نویسندگان
, , ,