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Simultaneous diophantine approximation [PDF]
Bulletin of the Australian Mathematical Society, 1972 AbstractUsing a method suggested by E. S. Barnes, it is shown that the simultaneous inequalities r(p — αr)2 < c, r(q — βr)2 < c have an infinity of integral solutions p, q, r (with r > 0), for arbitrary irrationals α and β, provided that c > 1/2.6394.
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On Best Simultaneous Approximation
Journal of Approximation Theory, 1997 Let \(X\) be a compact Hausdorff space, \(Y\) be a normed linear space, \(C(X, Y)\) be the vector space of continuous functions from \(X\) to \(Y\) and \(S\) be a subspace of \(C(X, Y).\) Suppose that \(C(X, Y)\) is normed with a given norm \(\| \cdot\| _A\) and that \(U\) is the unit ball of \((\mathbb R^n, \| \cdot\| _B).
Li, Chong, Watson, G.A
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Simultaneous approximation for Szász-Mirakian quasi-interpolants [PDF]
, 1983 summary:We obtain simultaneous approximation equivalence theorem for Szász-Mirakian quasi ...
Guo, Shunsheng +3 more
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Simultaneous Approximation on Affine Subspaces [PDF]
International Mathematics Research Notices, 2019 Abstract We solve the convergence case of the generalized Baker–Schmidt problem for simultaneous approximation on affine subspaces, under natural diophantine type conditions. In one of our theorems, we do not require monotonicity on the approximation function.
Jing-Jing Huang, Jason J Liu
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Best neural simultaneous approximation [PDF]
, 2020 For many years, approximation concepts has been investigated in view of neural networks for the several applications of the two topics. Researchers studied simultaneous approximation in the 2-normed space and proved essential theorems concern with ...
S. Bhaya, Eman +5 more
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Some Results on f-Simultaneous Chebyshev Approximation [PDF]
, 2016 Let X be Hausdorff topological vector space and f be a real valued continuous function on X: In this paper we introduce and study the concept of f-simultaneous approximation of a nonempty subset K of X as a generalization to the problem of simultaneous ...
Al-Sharif, Sh., Qaraman, Kh.
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Simultaneous Diophantine approximation
Duke Mathematical Journal, 1946 The simplest problems of Diophantine approximation relate to the approximation of a single irrational number 0 by rational numbers pjq, and the principal question is how small we can make the error 0 — pjq in relation to q for infinitely many approximations. It is well known that this question can be answered almost completely in terms of the continued
Davenport, H., Mahler, K.
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Fuzzy Best Simultaneous Approximation of a Finite Numbers of Functions [PDF]
Sahand Communications in Mathematical Analysis, 2019 Fuzzy best simultaneous approximation of a finite number of functions is considered. For this purpose, a fuzzy norm on $Cleft (X, Y right )$ and its fuzzy dual space and also the set of subgradients of a fuzzy norm are introduced.
Hossain Alizadeh Nazarkandi
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A Modification of the Mixed Joint Universality Theorem for a Class of Zeta Functions
Mathematics, 2022 The property of zeta functions on mixed joint universality in the Voronin’s sense states that any two holomorphic functions can be approximated simultaneously with an accuracy of ε>0 by suitable vertical shifts of the pair consisting the Riemann and ...
Roma Kačinskaitė +1 more
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Lower bounds for simultaneous Diophantine approximation constants [PDF]
, 1955 summary:After a brief exposition of the state-of-art of research on the (Euclidean) simultaneous Diophantine approximation constants $\theta _s$, new lower bounds are deduced for $\theta _6$ and $\theta _7$
Nowak, Werner Georg, J. V. Armitage
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