Results 1 to 10 of about 63 (46)

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   +8 more sources

Flett's mean value theorem in topological vector spaces [PDF]

International Journal of Mathematics and Mathematical Sciences, 2001
We prove some generalizations of Flett's mean value theorem for a class of Gateaux differentiable functions f:X→Y, where X and Y are topological vector spaces.
Robert C. Powers, Thomas Riedel, Prasanna K. Sahoo   +2 more
doaj   +7 more sources

On a functional equation related to a generalization of Flett's mean value theorem [PDF]

International Journal of Mathematics and Mathematical Sciences, 2000
In this paper, we characterize all the functions that attain their Flett mean value at a particular point between the endpoints of the interval under consideration. These functions turn out to be cubic polynomials and thus, we also characterize these.
T. Riedel, Maciej Sablik
doaj   +7 more sources

Some special cases on Stolarsky’s means [PDF]

Ratio Mathematica
In this paper we observe that one-parameter Stolarsky’s means (SM) are deduced from both the Mean Value Theorem for derivatives (MVTD) and the Mean Value Theorem for definite integrals (MVTI), and we study their elementary properties as the parameter ...
Cesare Palmisani
doaj   +3 more sources

Flett's Mean Value Theorem for Holomorphic Functions [PDF]

Mathematics Magazine, 1999
(1999). Flett's Mean Value Theorem for Holomorphic Functions. Mathematics Magazine: Vol. 72, No. 4, pp. 304-307.
R. M. Davitt, R. C. Powers, T. Riedel, P. K. Sahoo   +3 more
openaire   +2 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.
Hutník, Ondrej, Molnárová, Jana
openaire   +4 more sources

A Cauchy-type generalization of Flett's theorem

Demonstratio Mathematica, 2021
We prove a Cauchy-type generalization of Flett’s theorem and note its geometric interpretations. Several other mean value theorems extending further the result, which involve both real and complex functions, are also proved.
Markov Lubomir
doaj   +1 more source

The mean value theorem of Flett and divided differences

Journal of Mathematical Analysis and Applications, 2004
Flett's mean value theorem reads as follows: If \(f\) is differentiable on \([a,b]\) and \(f'(a)=f'(b)\), then there exists a point \(c\in(a,b)\) such that \[ f(c)-f(a)=f'(c)(c-a).\tag{11} \] After a careful analysis of divided differences on multiple knots, the authors rewrite as \([a,c,c;f]\) \(=0\) and give condensed representations of other Flett ...
Abel, Ulrich, Ivan, Mircea, Riedel, Thomas   +2 more
openaire   +3 more sources

Extended Generalized Flett's Mean Value Theorem

, 2016
6 ...
Pandey, Rupali, Padhye, Sahadeo
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A Survey in Mean Value Theorems [PDF]

, 1970
A variety of new mean value theorems are presented along with interesting proofs and generalizations of the standard theorems. Three proofs are given for the ordinary Mean Value Theorem for derivatives, the third of which is interesting in that it is ...
Neuser, David A.
core   +1 more source