The Asymptotic Property of Generalized Taylor Remainder

Chinese Quarterly Journal of Mathematics ›› 2004, Vol. 19 ›› Issue (3): 314-318.

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)；

Abstract

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

CLC Number:

O177.91

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

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