广义泰勒余项“中值点”的渐进性

数学季刊 ›› 2004, Vol. 19 ›› Issue (3): 314-318.

广义泰勒余项“中值点”的渐进性

Department of Mathematics and Information Science, Zhoukou Teacher's College, Zhoukou 466000, China ; College of Business Administration, Henan University, Kaifeng 475001, China

收稿日期:2002-01-15 出版日期:2004-09-30 发布日期:2024-03-14
作者简介:REN Li-shun(1958-),male,native of Zhoukou,Henan,an associate professor of Zhoukou Teacher's College,M.S.D.,engages in nonlinear functional analysis.
基金资助:
Supported by the Natural Seience Foundation of Henan Educational Committee(20031100036)；

The Asymptotic Property of Generalized Taylor Remainder "Mean Value Point"

Department of Mathematics and Information Science, Zhoukou Teacher's College, Zhoukou 466000, China ; College of Business Administration, Henan University, Kaifeng 475001, China

Received:2002-01-15 Online:2004-09-30 Published:2024-03-14
About author:REN Li-shun(1958-),male,native of Zhoukou,Henan,an associate professor of Zhoukou Teacher's College,M.S.D.,engages in nonlinear functional analysis.
Supported by:
Supported by the Natural Seience Foundation of Henan Educational Committee(20031100036)；

摘要/Abstract

摘要： This paper discussed asymptotic property of Taylor remainder "mean value point" in normed Linear space. The asymptotic progerty of "mean value point" is solved when f⁽ⁿ⁺ⁱ⁾(x₀)h⁽ⁿ⁺ⁱ⁾ = 0(i = 1, 2,..., p - 1) and f^(n+p)(x₀)h^(h+p) don’t exist. Meanwhile, achieve more general asymptotic estimation formula. Make many former results are just because of special case of the pager.

关键词: functional, F-derivative, Ga-derivative, mean , value , point, assymptotic , prop-
erty

Abstract: This paper discussed asymptotic property of Taylor remainder "mean value point" in normed Linear space. The asymptotic progerty of "mean value point" is solved when f⁽ⁿ⁺ⁱ⁾(x₀)h⁽ⁿ⁺ⁱ⁾ = 0(i = 1, 2,..., p - 1) and f^(n+p)(x₀)h^(h+p) don’t exist. Meanwhile, achieve more general asymptotic estimation formula. Make many former results are just because of special case of the pager.

Key words: functional, F-derivative, Ga-derivative, mean , value , point, assymptotic , prop-
erty

中图分类号:

O177.91

任立顺, 张彩玉. 广义泰勒余项“中值点”的渐进性[J]. 数学季刊, 2004, 19(3): 314-318.

REN Li-shun, ZHANG Cai-yu . The Asymptotic Property of Generalized Taylor Remainder "Mean Value Point"[J]. Chinese Quarterly Journal of Mathematics, 2004, 19(3): 314-318.

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