کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4615705 1339327 2014 19 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Bernstein–Durrmeyer operators with respect to arbitrary measure, II: Pointwise convergence
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Bernstein–Durrmeyer operators with respect to arbitrary measure, II: Pointwise convergence
چکیده انگلیسی

We consider the Bernstein–Durrmeyer operator Mn,ρMn,ρ with respect to an arbitrary measure ρ on the d  -dimensional simplex. This operator is a generalization of the well-known Bernstein–Durrmeyer operator with respect to the Lebesgue measure. We prove that (Mn,ρf)(x)→f(x)(Mn,ρf)(x)→f(x) as n→∞n→∞ at each point x∈suppρ if f is bounded on supp ρ and continuous at x. Moreover, the convergence is uniform in any compact set in the interior of supp ρ.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 418, Issue 2, 15 October 2014, Pages 734–752
نویسندگان
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