کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8900229 1631557 2018 42 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Interpolatory pointwise estimates for monotone polynomial approximation
ترجمه فارسی عنوان
ناسازگاری درونی برای تخمین تقریبی چند جمله ای یکنواخت
کلمات کلیدی
تقریب چند جمله ای مونوتونی، درجه تقریبی، برآوردهای متقابل نوع جکسون،
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
چکیده انگلیسی
Given a nondecreasing function f on [−1,1], we investigate how well it can be approximated by nondecreasing algebraic polynomials that interpolate it at ±1. We establish pointwise estimates of the approximation error by such polynomials that yield interpolation at the endpoints (i.e., the estimates become zero at ±1). We call such estimates “interpolatory estimates”. In 1985, DeVore and Yu were the first to obtain this kind of results for monotone polynomial approximation. Their estimates involved the second modulus of smoothness ω2(f,⋅) of f evaluated at 1−x2/n and were valid for all n≥1. The current paper is devoted to proving that if f∈Cr[−1,1], r≥1, then the interpolatory estimates are valid for the second modulus of smoothness of f(r), however, only for n≥N with N=N(f,r), since it is known that such estimates are in general invalid with N independent of f. Given a number α>0, we write α=r+β where r is a nonnegative integer and 0<β≤1, and denote by Lip⁎α the class of all functions f on [−1,1] such that ω2(f(r),t)=O(tβ). Then, one important corollary of the main theorem in this paper is the following result that has been an open problem for α≥2 since 1985:
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 459, Issue 2, 15 March 2018, Pages 1260-1295
نویسندگان
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