Results 21 to 30 of about 64,486 (162)
Hyers–Ulam Stability of Two-Dimensional Flett’s Mean Value Points
Mathematics, 2019 If a differentiable function f : [ a , b ] → R and a point η ∈ [ a , b ] satisfy f ( η ) − f ( a ) = f ′ ( η ) ( η − a ) , then the point η is called a Flett ...
Soon-Mo Jung, Ji-Hye Kim, Young Woo Nam
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Surveys in Mathematics and its Applications, 2023 We present a streamlined, slightly modified version, in the two-variable situation, of a beautiful, but not so well known, theory by Bögel, already from the 1930s, on an alternative higher dimensional calculus of real functions, a double calculus, which ...
Patrik Lundström
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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
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Some mean value theorems as consequences of the Darboux property [PDF]
Mathematica Bohemica, 2017 The aim of the paper is to present some mean value theorems obtained as consequences of the intermediate value property. First, we will prove that any nonextremum value of a Darboux function can be represented as an arithmetic, geometric or harmonic mean
Dan Ştefan Marinescu, Mihai Monea
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Second order differentiability of the intermediate-point function in Cauchy's mean-value theorem
Journal of Numerical Analysis and Approximation Theory, 2015 If the functions \(f,g:I\rightarrow \mathbb{R}\) are differentiable on the interval \(I\subseteq \mathbb{R}\), \(a\in I,\) then there exists a function \(\bar{c}:I\rightarrow I\) such that $$ \left[ f\left( x\right) -f\left( a\right) \right] g ...
Beatrix-Mihaela Pop, Dorel Duca
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The First Mean Value Theorem for Integrals [PDF]
Formalized Mathematics, 2008 For simplicity, we use the following convention: X is a non empty set, S is a σ-field of subsets of X, M is a σ-measure on S, f , g are partial functions from X to R, and E is an element of S. One can prove the following three propositions: (1) If for every element x of X such that x ∈ dom f holds f(x) ≤ g(x), then g − f is non-negative.
Keiko Narita +2 more
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Symmetric partially Darboux functions and multiple points mean value results [PDF]
Mathematica BohemicaWe consider mean value results for symmetric multivariable functions whose partial functions satisfy the intermediate value property.
Viorel Vîjîitu
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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
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Addendum to Alternative analysis generated by a differential equation
Electronic Journal of Qualitative Theory of Differential Equations, 2004 This addendum concerns the paper of the above title found in EJQTDE No. 2 (2003 ). On page 3, before (2.2), instead of "Applying the mean value theorem" it should read "By simple calculations".
Z. Z. Khukhunashvili +1 more
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On a mean value theorem connected with Hermite-Hadamard's inequality
Journal of Numerical Analysis and Approximation Theory, 2004 In this paper we prove a mean-value theorem for integral calculus, then we demonstrate properties of the mean point. In the end we give an extension of Hermite-Hadamard's inequality.
Ovidiu T. Pop
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