Baskakov operators and Jacobi weights: pointwise estimates

Bustamante, Jorge; Merino-García, Juan Jesús; Quesada, José M.

doi:10.1186/s13660-021-02653-4

Cited by 3 publications

(1 citation statement)

References 13 publications

(21 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Notice that the arguments of Wafi and Khatoon can not be used to obtain an estimate in the weighted norm over all the interval [0, ∞). We remark that some results related with Szász and Baskakov operators were given recently in [1] and [4]. Throughout the paper we set…”

Section: Introduction For | T |< 1 Let Us Consider the Expansionmentioning

confidence: 99%

Approximation of functions and Mihesan operators

Bustamante

2023

MFC

Self Cite

View full text Add to dashboard Cite

<p style='text-indent:20px;'>For real numbers <inline-formula><tex-math id="M1">\begin{document}$ a,q\geq 0 $\end{document}</tex-math></inline-formula> and a weight <inline-formula><tex-math id="M2">\begin{document}$ \varrho(x) = 1/(1+x)^q $\end{document}</tex-math></inline-formula>, the author provides necessary and sufficient conditions for a function <inline-formula><tex-math id="M3">\begin{document}$ f\in C[0,\infty) $\end{document}</tex-math></inline-formula> in order to <inline-formula><tex-math id="M4">\begin{document}$ \sup_{x\geq 0}\mid \varrho(x)(B_n^a(f,x)-f(x))\mid \to 0 $\end{document}</tex-math></inline-formula> as <inline-formula><tex-math id="M5">\begin{document}$ n\to \infty $\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M6">\begin{document}$ B_n^a(f) $\end{document}</tex-math></inline-formula> is the Mihesan operator. In particular, it is proved that Mihesan operators behave similar to the classical Baskakov operators.</p>

show abstract

Section: Introduction For | T |< 1 Let Us Consider the Expansionmentioning

confidence: 99%