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Let $f$ be a real function defined on the interval $[0,1]$ which is constant on $(a,b)\subset [0,1]$, and let $B_nf$ be its associated $n$th Bernstein polynomial. We prove that, for any $x\in (a,b)$, $|B_nf(x)-f(x)|$ converges to $0$ as $n\rightarrow
Externí odkaz:
http://arxiv.org/abs/2411.10135
We obtain approximation results for general positive linear operators satisfying mild conditions, when acting on discontinuous functions and absolutely continuous functions having discontinuous derivatives. The upper bounds, given in terms of a local
Externí odkaz:
http://arxiv.org/abs/2410.19893
We obtain strong converse inequalities for the Bernstein polynomials with explicit asymptotic constants. We give different estimation procedures in the central and non-central regions of [0,1]. The main ingredients in our approach are the following:
Externí odkaz:
http://arxiv.org/abs/2409.03382
Fractional binomial distributions induced by the generalized binomial theorem and their applications
Autor:
Hino, Masanori, Namba, Ryuya
A generalized binomial theorem was established by Hara and Hino [Bull. London Math. Soc. 42 (2010), 467-477] for proving the neo-classical inequality. We introduce a new fractional analogue of the binomial distribution on the basis of the generalized
Externí odkaz:
http://arxiv.org/abs/2408.12011
In this paper we present commutativity results for a general class of Szasz-Mirakjan-Durrmeyer type operators and associated differential operators and investigate their eigenfunctions.
Externí odkaz:
http://arxiv.org/abs/2407.21722
Autor:
Patel, Prashantkumar
This note aims to present novel positive linear operators involving the Wright function. Furthermore, the present research established the moments of these newly defined operators and estimated the convergence rate using the classical modulus of cont
Externí odkaz:
http://arxiv.org/abs/2404.04651
Autor:
An, Congpei, Ran, Jiashu
This paper considers the so-called concept of hyperinterpolation-class, i.e., the set of all operators derived from the hyperinterpolation operator on the unit sphere. Concretely, we select four different elements in the hyperinterpolation-class, nam
Externí odkaz:
http://arxiv.org/abs/2404.00523
Autor:
Yadav, Rishikesh, Mauroy, Alexandre
The Koopman operator approach provides a powerful linear description of nonlinear dynamical systems in terms of the evolution of observables. While the operator is typically infinite-dimensional, it is crucial to develop finite-dimensional approximat
Externí odkaz:
http://arxiv.org/abs/2403.02438
Autor:
Acu, Ana-Maria, Gonska, Heiner
Extending an earlier estimate for the degree of approximation of overiterated univariate Bernstein operators towards the same operator of degree one, it is shown that an analogous result holds in the $d$-variate case. The method employed can be carri
Externí odkaz:
http://arxiv.org/abs/2402.16485
Iterates of multidimensional Bernstein-type operators and diffusion processes in population genetics
Autor:
Hirano, Takatoshi, Namba, Ryuya
The Bernstein operator is known as a typical example of positive linear operators which uniformly approximates continuous functions on $[0, 1]$. In the present paper, we introduce a multidimensional extension of the Bernstein operator which is associ
Externí odkaz:
http://arxiv.org/abs/2310.13983