Results 41 to 50 of about 1,900,675 (267)
Functional equations and the Cauchy mean value theorem [PDF]
, 2015 The aim of this note is to characterize all pairs of sufficiently smooth functions for which the mean value in the Cauchy mean value theorem is taken at a point which has a well-determined position in the interval.
Z. Balogh, O. O. Ibrogimov, B. Mityagin
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Mean-value theorem for vector-valued functions [PDF]
Mathematica Bohemica, 2012 Summary: For a differentiable function \(f\: I\rightarrow \mathbb {R}^k\), where \(I\) is a real interval and \(k\in \mathbb {N}\), a counterpart of the Lagrange mean-value theorem is presented. Necessary and sufficient conditions for the existence of a mean \(M\: I^2\rightarrow I\) such that \[ f(x)-f(y)=(x-y)f'(M(x,y)),\; x,y\in I, \] are given ...
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Constraints on stochastic heat probability prescribed by exchange fluctuation theorems
Results in Physics, 2020 The amount of heat transfer from one body to another during a finite time contact is a stochastic variable. The observed probability of heat can be prescribed by the exchange fluctuation theorem and its extensions; however, it should be stipulated in ...
Takuya Yamano
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Mean Value Theorems for Vector Valued Functions [PDF]
Proceedings of the Edinburgh Mathematical Society, 1965 The object of this paper is to give a generalisation to vector valued functions of the classical mean value theorem of differential calculus. In that theorem we havefor some c in the open interval a, b when f is a real valued function which is continuous on the closed interval a, b and differentiable on the open interval.
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Hyers-Ulam Stability of Lagrange’s Mean Value Points in Two Variables
Mathematics, 2018 Using a theorem of Ulam and Hyers, we will prove the Hyers-Ulam stability of two-dimensional Lagrange’s mean value points ( η , ξ ) which satisfy the equation, f ( u , v ) − f ( p , q ) = ( u − p ) f x ( &#
Soon-Mo Jung, Ji-Hye Kim
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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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General equilibrium of Bertrand game: A spatial computational approach
AIMS Mathematics, 2021 In this paper, the competitive equilibrium of the Bertrand game is discussed with bounded rationality and the utility function. When the parameters changing and the number of firms increasing, the competitive equilibrium valve of Bertrand duopoly game is
Bingyuan Gao, Yaxin Zheng, Jieyu Huang
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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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Mathematical Biosciences and Engineering, 2023 We propose a fractional order model for human papillomavirus (HPV) dynamics, including the effects of vaccination and public health education on developing cervical cancer.
Simphiwe M. Simelane +3 more
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Optimal mean value estimates beyond Vinogradov's mean value theorem [PDF]
, 2019 We establish improved mean value estimates associated with the number of integer solutions of certain systems of diagonal equations, in some instances attaining the sharpest conjectured conclusions.
Brandes, Julia, Wooley, Trevor D.
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