Results 1 to 10 of about 47 (38)
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
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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 +2 more
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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
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A Cauchy-type generalization of Flett's theorem [PDF]
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
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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
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On Generalizations of Flett's Theorem
Real Analysis Exchange, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jędrzejewska, Inga +1 more
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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 +2 more
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Conformable Flett’s theorem and Sahoo and Riedel theorem
Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2023 Since fractional analysis has attracted considerable interest by virtue of their ability to model complex phenomena, it is crucial to investigate properties of fractional derivatives. In this research, accordingly, we first give the extension of Flett's theorem and Sahoo and Riedel theorem to conformable derivative as a variety of conformable mean ...
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AN EXTENSION OF A THEOREM OF FLETT
Demonstratio Mathematica, 1999 \textit{T. M. Flett} [Math. Gaz. 42, 38-39 (1958)] proved the following variant of the Lagrange mean value theorem: If \(f\) is differentiable in \([a,b]\) with \(f'(a)=f'(b)\), then there is an \(\eta \in (a,b)\) such that \(f(\eta)-f(a) = (\eta-a) f'(\eta)\). This was refined by \textit{P. K. Sahoo} and \textit{T.
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Some Variants of Wayment's Mean Value Theorem for Integrals
Selecciones MatemáticasThis 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
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