Results 21 to 30 of about 10,448,653 (237)
Effective Vinogradov's mean value theorem via efficient boxing [PDF]
Journal of Number Theory, 2016 We combine Wooley's efficient congruencing method with earlier work of Vinogradov and Hua to get effective bounds on Vinogradov's mean value theorem.
R. Steiner
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Sensitivity of the “intermediate point” in the mean value theorem: an approach via the Legendre-Fenchel transformation [PDF]
ESAIM: Proceedings and Surveys, 2021 We study the sensitivity, essentially the differentiability, of the so-called “intermediate point” c in the classical mean value theorem fa-f(b)b-a=f'(c)$ \frac{f(a)-f(b)}{b-a}={f}^{\prime}(c)$we provide the expression of its gradient ∇c(d,d), thus ...
Hiriart-Urruty Jean-Baptiste
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On Multivariate Fractional Taylor’s and Cauchy’ Mean Value Theorem
Journal of Mathematical Study, 2019 In this paper, a generalized multivariate fractional Taylor’s and Cauchy’s mean value theorem of the kind f (x,y)= n ∑ j=0 Djα f (x0,y0) Γ(jα+1) +Rn(ξ,η), f (x,y)− n ∑ j=0 Djα f (x0,y0) Γ(jα+1) g(x,y)− n ∑ j=0 Dg(x0,y0) Γ(jα+1) = Rn(ξ,η) Tα n (ξ,η ...
Jin-Fa Cheng
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The Bolzano mean-value theorem and partial differential equations [PDF]
, 2016 We study the existence of solutions to abstract equations of the form 0 = A u + F ( u ) , u ∈ K ⊂ E , where A is an abstract differential operator acting in a Banach space E, K is a closed convex set of constraints being invariant with respect to ...
W. Kryszewski, Jakub Siemianowski
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Flett's mean value theorem in topological vector spaces
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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Error term of the mean value theorem for binary Egyptian fractions
Open Mathematics, 2020 In this article, the error term of the mean value theorem for binary Egyptian fractions is studied. An error term of prime number theorem type is obtained unconditionally. Under Riemann hypothesis, a power saving can be obtained.
Xiao Xuanxuan, Zhai Wenguang
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The cubic case of Vinogradov’s mean value theorem [PDF]
Essential Number Theory, 2015 This is an expository paper, giving a simplified proof of the cubic case of the main conjecture for Vinogradov's mean value theorem.
D. R. Heath-Brown
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Equation of Finite Change and Structural Analysis of Mean Value
Axioms, 2023 This paper describes a problem of finding the contributions of multiple variables to a change in their function. Such a problem is well known in economics, for example, in the decomposition of a change in the mean price via the varying in time prices and
Stan Lipovetsky
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MEAN VALUES, MOMENTS, MOMENT RATIOS AND A GENERALIZED MEAN VALUE THEOREM FOR SIZE DISTRIBUTIONS
Ceramics-Silikáty, 2019 Generalized mean values of size distributions are defined via the general power mean, using Kronecker’s delta to allow for the geometric mean. Special cases of these generalized mean values are the superarithmetic, arithmetic, geometric, harmonic and ...
W. Pabst
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