Abstract
We investigate the rate of convergence of the operators introduced by Singh et al. (Linear Multilinear Algebra, 2022. https://doi.org/10.1080/03081087.2021.1960260) for functions of a polynomial growth. By using Steklov means, we obtain an estimate of error for these operators in terms of the modulus of continuity of order two. We derive an asymptotic theorem of Voronovskaja type and its quantitative form. Further, we modify these operators to examine the approximation of smooth functions in the above polynomial weighted space, i.e. a space of functions under a norm that involves multiplication by a polynomial function referred to as the weight and show that we achieve better approximation. We also discuss the convergence in the Lipschitz space and a Voronovskaja type asymptotic result.
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The authors are extremely grateful to the learned reviewers for a very careful reading of the manuscript and making invaluable suggestions and comments leading to an overall improvement in the presentation of the paper.
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Agrawal, P.N., Baxhaku, B. & Chauhan, R. q-Gamma Type Operators for Approximating Functions of a Polynomial Growth. Iran J Sci 47, 1367–1377 (2023). https://doi.org/10.1007/s40995-023-01507-6
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DOI: https://doi.org/10.1007/s40995-023-01507-6
Keywords
- Gamma type operators
- Modulus of continuity
- Polynomial weighted space
- Rate of convergence
- Steklov means
- Voronovskaja type theorem