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A general mean value theorem [PDF]
Publicationes Mathematicae Debrecen, 2016 In this note a general a Cauchy-type mean value theorem for the ratio of functional determinants is offered. It generalizes Cauchy's and Taylor's mean value theorems as well as other classical mean value theorems.
Páles, Zsolt
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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
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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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Functional equations and the Cauchy mean value theorem [PDF]
Aequationes Mathematicae, 2016 Zoltán M Balogh
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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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A Theorem on Mean-Value Iterations [PDF]
Proceedings of the American Mathematical Society, 1971 In this paper we consider a function which continuously maps a closed interval of the real line into itself. It is shown that a particular mean-value iterative scheme always converges to a fixed point. The result is known for functions which have a unique fixed point. This condition is not required here.
Franks, R. L., Marzec, R. P.
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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
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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
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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 +1 more
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Vinogradov's mean value theorem via efficient congruencing [PDF]
, 2011 We obtain estimates for Vinogradov's integral which for the first time approach those conjectured to be the best possible. Several applications of these new bounds are provided.
Arkhipov +13 more
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