Results 11 to 20 of about 10,448,653 (237)

Functional equations and the Cauchy mean value theorem [PDF]

, 2015
The aim of this note is to characterize all pairs of sufficiently smooth functions for which the mean value in the Cauchy mean value theorem is taken at a point which has a well-determined position in the interval.
Z. Balogh, O. O. Ibrogimov, B. Mityagin
semanticscholar   +5 more sources

On Generalized Flett's Mean Value Theorem [PDF]

International Journal of Mathematics and Mathematical Sciences, 2012
We present a new proof of generalized Flett's mean value theorem due to Pawlikowska (from 1999) using only the original Flett's mean value theorem. Also, a Trahan-type condition is established in general case.
Jana Molnárová
doaj   +2 more sources

Analogues of Fermat's extreme value theorem and Cauchy's mean value theorem in commutative algebras

Researches in Mathematics
In this article, we prove analogues of classical Fermat's extreme value theorem and Cauchy's mean value theorem for functions taking values in commutative algebras.
V. Shpakivskyi
doaj   +2 more sources

On the F.Smarandache LCM function and its mean value [PDF]

, 2007
The main purpose of this paper is using the elementary methods to study the mean value properties of ln SL(n), and give a sharper asymptotic formula for ...
Li, Jianghua, Liu, Yanyan
core   +3 more sources

The Vinogradov Mean Value Theorem (after Wooley, and Bourgain, Demeter and Guth) [PDF]

Astérisque, 2017
This is the expository essay that accompanies my Bourbaki Seminar on 17 June 2017 on the landmark proof of the Vinogradov Mean Value Theorem, and the two approaches developed in the work of Wooley and of Bourgain, Demeter and Guth.
Lillian B. Pierce
semanticscholar   +1 more source

Vinogradov's mean value theorem via efficient congruencing [PDF]

, 2012
We obtain estimates for Vinogradov's integral that for the first time approach those conjectured to be the best possible. Several applications of these new bounds are provided.
Wooley, Trevor D., Trevor D. Wooley
core   +1 more source

The Mean Value Theorem in the Context of Generalized Approach to Differentiability

Mathematics, 2023
The article is a natural continuation of the systematic research of the properties of the generalized concept of differentiability for functions with a domain X⊂Rn that is not necessarily open, at points that allow a neighbourhood ray in the domain.
Nikola Koceić-Bilan, Ivančica Mirošević   +1 more
doaj   +1 more source

Mean-value theorem for vector-valued functions [PDF]

, 2012
summary:For a differentiable function ${\bf f}\colon I\rightarrow \mathbb {R}^{k},$ where $I$ is a real interval and $k\in \mathbb {N}$, a counterpart of the Lagrange mean-value theorem is presented. Necessary and sufficient conditions for the existence
Matkowski, Janusz
core   +1 more source

On some mean value theorem via covering argument

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020
We show how the full covering argument can be used to prove some type of Cauchy mean value theorem.
Sokołowski Dariusz
doaj   +1 more source

Value distribution of the F.Smarandache LCM function [PDF]

, 2006
The main purpose of this paper is using the elementary methods to study the value distribution properties of the function SL(n), and give a sharper value distribution ...
Chen, Jianbin, Jianbin Chen
core   +1 more source