Convergence properties of generalized Lupaş-Kantorovich operators

In the present paper, we consider the Kantorovich modification of generalized Lupaş operators, whose construction depends on a continuously differentiable, increasing and unbounded function $\rho$. For these new operators we give weighted approximation, Voronovskaya type theorem, quantitative estimates for the local approximation.

Approximation properties of a new family of Gamma operators and their applications

The present paper introduces a new modification of Gamma operators that protects polynomials in the sense of the Bohman–Korovkin theorem. In order to examine their approximation behaviours, the approximation properties of the newly introduced operators such as Voronovskaya-type theorems, rate of convergence, weighted approximation, and pointwise estimates are presented. Finally, we present some numerical examples to verify that the newly constructed operators are an approximation procedure.

Approximation by mixed positive linear operators based on second-kind beta transform

In this paper, we consider mixed approximation operators based on second-kind beta transform using Szász–Mirakjan operators. For the proposed operators, we establish some direct results, Voronovskaya-type theorem, quantitative Voronovskaya-type theorem, Grüss–Voronovskaya-type theorem, weighted approximation and functions of bounded variation.

Approximation by a new sequence of operators involving Apostol-Genocchi polynomials

The main objective of this paper is to construct a new sequence of operators involving Apostol-Genocchi polynomials based on certain parameters. We investigate the rate of convergence of the operators given in this paper using second-order modulus of continuity and Voronovskaja type approximation theorem. Moreover, we find weighted approximation result of the given operators. Finally, we derive the Kantorovich variant of the given operators and discussed the approximation results.

Convergence of Certain Baskakov Operators of Integral Type

In the present paper, we propose a Baskakov operator of integral type using a function φ on [0,∞) with the properties: φ(0)=0,φ′>0 on [0,∞) and limx→∞φ(x)=∞. The proposed operators reproduce the function φ and constant functions. For the constructed operator, some approximation properties are studied. Voronovskaja asymptotic type formulas for the proposed operator and its derivative are also considered. In the last section, the interest is focused on weighted approximation properties, and a weighted convergence theorem of Korovkin’s type on unbounded intervals is obtained. The results can be extended on the interval (−∞,0] (the symmetric of the interval [0,∞) from the origin).

Reflecting on the COVID-19 Surgical Literature Surge: A Scoping Review of Pandemic Otolaryngology Publications

Objective To assess the high-volume 2020 COVID-19-related surgical literature, with special attention to otolaryngology articles in regard to content, level of evidence, citations, and public attention. Study Design A scoping literature review was performed with PubMed and Web of Science, including articles pertaining to COVID-19 and surgical specialties (March 20–May 19, 2020) or otolaryngologic subspecialties (March 20–December 31, 2020). Setting Scoping literature review. Methods Otolaryngology-specific COVID-19-related articles were reviewed for publication date, county of origin, subspecialty, content, level of evidence, and Altmetric Attention Score (a weighted approximation of online attention received). Data were analyzed with Pearson correlation coefficients, analysis of variance, independent t tests, and univariable and logistic regressions. Results This review included 773 early COVID-19 surgical articles and 907 otolaryngology-specific COVID-19-related articles from 2020. Otolaryngology was the most represented surgical specialty within the early COVID-19-related surgical literature (30.4%). The otolaryngology-specific COVID-19 surgical literature responsively reflects the unique concerns within each otolaryngologic subspecialty. Although this literature was largely based on expert opinion (64.5%), articles with stronger levels of evidence received significantly more citations (on Web of Science and Google Scholar, P < .001 for both) and public attention (according to Altmetric Attention Scores, P < .001). Conclusion Despite concerns of a surge in underrefereed publications during the COVID-19 pandemic, our review of the surgical literature offers some degree of reassurance. Specifically, the COVID-19 otolaryngology literature responsively reflects the unique concerns and needs of the field, and more scholarly citations and greater online attention have been given to articles offering stronger levels of scientific evidence.

Certain approximation properties of Brenke polynomials using Jakimovski–Leviatan operators

In this article, we establish the approximation by Durrmeyer type Jakimovski–Leviatan operators involving the Brenke type polynomials. The positive linear operators are constructed for the Brenke polynomials, and thus approximation properties for these polynomials are obtained. The order of convergence and the weighted approximation are also considered. Finally, the Voronovskaya type theorem is demonstrated for some particular case of these polynomials.