King-type operators related to squared Szasz-Mirakyan basis

Holhoş, Adrian

doi:10.24193/subbmath.2020.2.09

Cited by 5 publications

(2 citation statements)

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“…One can refer to the previous articles. [18][19][20][21] In this article, we use a similar approach to present a modification of operators (1.3) such that the modified operator preserves the test function e s (x) = x s , s ∈ N. We begin by setting ℘ n, s (x) ∈ (0, ∞) and rewriting operators (1.3) as…”

Section: Introductionmentioning

confidence: 99%

“…Inspired by this approach, many other mathematicians devoted their research to produce modifications of well‐known approximation processes fixing certain (polynomial, exponential, or more general) functions and to study their approximation and shape preserving properties. One can refer to the previous articles 18–21 . In this article, we use a similar approach to present a modification of operators () such that the modified operator preserves the test function

e_{s} false(x false) = x^{s}, s \in ℕ

.…”

Section: Introductionmentioning

confidence: 99%

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Convergence estimates of certain gamma type operators

Mishra

Deo

2021

Math Methods in App Sciences

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The present paper deals with a modified form of gamma type operators that preserve the test functions es=ts,3.0235pts∈ℕ and estimation of their approximation properties. We begin by determining the convergence rate of the proposed operators in the sense of the usual modulus of continuity and Peetre's K‐functional. Further, the degree of approximation is also established for the function of bounded variation. We also illustrate via figures and tables that the proposed modification provides a better approximation for preserving the test function e3.

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Section: Introductionmentioning

confidence: 99%

e_{s} false(x false) = x^{s}, s \in ℕ

.…”

Section: Introductionmentioning

confidence: 99%

Convergence estimates of certain gamma type operators

Mishra

Deo

2021

Math Methods in App Sciences

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A Voronovskaya-type theorem in simultaneous approximation

Holhoş

2021

Period Math Hung

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Decolorization of Congo Red and Reactive Black 5 Dyes with Horseradish Peroxidase-Immobilized Cross-Linked Polymeric Microbeads

Zhumabekova,

Noma,

Tümay Özer

et al. 2024

Arab J Sci Eng

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In this study, the efficiency of poly(ethylene glycol dimethacrylate-N-methacryloyl-amido-l-tryptophan methyl ester) [PEDMT] microbeads (in the diameter range of 106–180 µm) as a support material for HRP immobilization was evaluated and the immobilized-HRP enzyme was used for decolorization of Congo Red (CR) and Reactive Black 5 (RB5) dyes. The specific surface area of the PEDMT microbeads was 1103 m2 g−1, which is very high. The PEDMT microbeads had a pore volume and pore size of 1.94 cm3 g−1 and 9.99–55.3 Å, respectively. The chemical compositions of the PEDMT and PEDMT–HRP microbead surfaces were analyzed using X-ray photoelectron spectroscopy (XPS). Immobilization yield, activity yield, and immobilization efficiency were 84.9 ± 2.1, 73.8 ± 5.9%, and 86.9 ± 6.9%, respectively. Optimum pH (6.0), temperature (45 °C and 50 °C for free and immobilized enzyme), H2O2 concentration (3% v/v) were investigated in detail. Thermal and storage stability was increased after immobilization and immobilized enzyme preserved more than 55% of its initial activity even after 10 consecutive uses. Decolorization studies were also performed by investigating the effects of pH, CR, and RB5 concentration, enzyme amount, H2O2 concentration, contact time on decolorization efficiency. The decolorization efficiency for CR and RB5 by PEDMT–HRP was 98.20% and 47.99% after 30 min at pH 6.0 and 45 °C. The immobilized-HRP retained 89% and 27% of its initial activity after three repeated cycles with CR and RB5, respectively. The PEDMT microbeads with high surface area, porosity, durability, and reusability exactly met the requirements for HRP immobilization and dye decolorization.

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King-type operators related to squared Szasz-Mirakyan basis

Abstract: In this paper we study some approximation properties of a sequence of positive linear operators defined by means of the squared Szász-Mirakyan basis and prove that these operators behave better than the classical Szász-Mirakyan operators.

Cited by 5 publications

References 11 publications

Convergence estimates of certain gamma type operators

Convergence estimates of certain gamma type operators

A Voronovskaya-type theorem in simultaneous approximation

Decolorization of Congo Red and Reactive Black 5 Dyes with Horseradish Peroxidase-Immobilized Cross-Linked Polymeric Microbeads

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