A Study of King-Type Operators Connecting Wavelet and Quantum Calculus: Numerical and Graphical Analysis
- 1Department of Mathematics, Faculty of Science, University of Ostrava, Mlýnská 702/5, Moravská Ostrava, 702 00 Ostrava, Czech Republic
- 2Department of Mathematics, School of Computer Science & Artificial Intelligence, SR University, Warangal 506371, Telangana, India
- 3Department of Mathematics, University Center for Research and Development, Chandigarh University, Mohali 140413, Punjab, India
Abstract
This paper introduces a new class of King-type wavelet-assisted Kantorovich q-Baskakov operators, built to address the observation that classical operators of this type typically fail to reproduce the quadratic test function exactly. Moment formulas are derived for these operators, and a weighted Korovkin-type theorem is used to establish convergence. The speed of pointwise convergence is then quantified with the help of the modulus of smoothness and Lipschitz-type maximal function spaces; the resulting convergence factor δnqn turns out to be smaller than that reported for earlier q-Baskakov constructions, indicating an improvement in approximation power. Beyond the theoretical development, a numerical and graphical investigation plots the pointwise error |Yn,q*f(z)−f(z)| for several parameter pairs (n,q), with the error found to decrease steadily as n increases and q approaches 1, consistent with the theoretical estimates. Implementation details accompany this study to make the computations reproducible and to connect the abstract approximation-theoretic results with their practical execution.
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BibTeX
@article{aymanmursaleen2026study,
title = {{A Study of King-Type Operators Connecting Wavelet and Quantum Calculus: Numerical and Graphical Analysis}},
author = {Mohammad Ayman-Mursaleen and Inzamamul Haque and Nadeem Rao},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14193627},
url = {https://www.mdpi.com/2227-7390/14/19/3627},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A Study of King-Type Operators Connecting Wavelet and Quantum Calculus: Numerical and Graphical Analysis
AU - Mohammad Ayman-Mursaleen
AU - Inzamamul Haque
AU - Nadeem Rao
PY - 2026
DA - 2026/10/07
JO - Mathematics
DO - 10.3390/math14193627
UR - https://www.mdpi.com/2227-7390/14/19/3627
AB - This paper introduces a new class of King-type wavelet-assisted Kantorovich q-Baskakov operators, built to address the observation that classical operators of this type typically fail to reproduce the quadratic test function exactly. Moment formulas are derived for these operators, and a weighted Korovkin-type theorem is used to establish convergence. The speed of pointwise convergence is then quantified with the help of the modulus of smoothness and Lipschitz-type maximal function spaces; the resulting convergence factor δnqn turns out to be smaller than that reported for earlier q-Baskakov constructions, indicating an improvement in approximation power. Beyond the theoretical development, a numerical and graphical investigation plots the pointwise error |Yn,q*f(z)−f(z)| for several parameter pairs (n,q), with the error found to decrease steadily as n increases and q approaches 1, consistent with the theoretical estimates. Implementation details accompany this study to make the computations reproducible and to connect the abstract approximation-theoretic results with their practical execution.
SN - 2227-7390
ER -