Results 1 to 10 of about 1,900,675 (267)

The mean value theorem and Taylor’s theorem for fractional derivatives with Mittag–Leffler kernel [PDF]

Advances in Difference Equations, 2018
We establish analogues of the mean value theorem and Taylor’s theorem for fractional differential operators defined using a Mittag–Leffler kernel. We formulate a new model for the fractional Boussinesq equation by using this new Taylor series expansion.
Arran Fernandez, Dumitru Baleanu
doaj   +3 more sources

A general mean value theorem [PDF]

Publicationes Mathematicae Debrecen, 2015
K
Páles, Zsolt
core   +8 more sources

On Flett’s mean value theorem [PDF]

Aequationes mathematicae, 2014
Mean value theorems play an important role in differential and integral calculus as they are a powerful tool for solving problems in mathematical analysis. The authors of the present paper provide a thorough study of Flett's mean value theorem of a real-valued function of one real variable.
Ondrej Hutník, Jana Molnárová
semanticscholar   +5 more sources

APPROXIMATING THE MAIN CONJECTURE IN VINOGRADOV'S MEAN VALUE THEOREM [PDF]

, 2016
We apply multigrade efficient congruencing to estimate Vinogradov's integral of degree $k$ for moments of order $2s$, establishing strongly diagonal behaviour for $1\le s\le \frac{1}{2}k(k+1)-\frac{1}{3}k+o(k)$.
Trevor D. Wooley
core   +7 more sources

Some variants of Lagrange’s mean value theorem

Selecciones Matemáticas, 2020
In this note we prove some variants of Lagrange’s mean value theorem. The main tools to prove these results are some elementary auxiliary functions.
German Lozada-Cruz
doaj   +2 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   +4 more sources

Some Variants of Wayment's Mean Value Theorem for Integrals

Selecciones Matemáticas
This note deals with some variants of Wayment’s Mean Value Theorem for integrals. Our approach is rather elementary and does not use advanced techniques from analysis. The simple auxiliary functions were used to prove the results.
German Lozada-Cruz
doaj   +3 more sources

Proof of Lagrange Mean Value Theorem and its Application in Text Design

Chemical Engineering Transactions, 2016
At present, there are a lot of papers on Lagrange mean value theorem proving method, the paper On the application of the theorem is not in a few, but text designs from the perspective of curriculum explore proving a theorem and its application to the ...
J.H. Li
doaj   +2 more sources

Mean value theorem for holomorphic functions

Electronic Journal of Differential Equations, 2012
This article presents a generalization of Myers' theorem and when the boundary assumption f'(a)=f'(b) is removed, and to prove this result for holomorphic functions of one complex variable.
Devrim Cakmak, Aydin Tiryaki
doaj   +3 more sources

On a basic mean value Theorem with explicit exponents [PDF]

, 2020
In this paper we follow a paper from A. Sedunova (2017) regarding R. C. Vaughan's basic mean value Theorem (Acta Arith. 1980) to improve and complete a more general demonstration for a suitable class of arithmetic functions as started by A. C.
Ferrari, Matteo
core   +2 more sources