Abstract
This paper is a continuation of the work done by Deo et al. (Appl. Math. Comput. 273, 281–289, 2016), in which the authors have established some approximation properties of the Stancu–Kantorovich operators based on Pólya–Eggenberger distribution. We obtain some direct results for these operators by means of the Lipschitz class function, the modulus of continuity and the weighted space. Also, we study an approximation theorem with the aid of the unified Ditzian–Totik modulus of smoothness \(\omega _{\phi ^{\tau }}(f;t),\,\,\,0\le \tau \le 1\) and the rate of convergence of the operators for the functions having a derivative which is locally of bounded variation on \([0,\infty )\).
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Acknowledgements
The work of the second author was financed from Lucian Blaga University of Sibiu research Grants LBUS-IRG-2017-03 and the third author is thankful to “The Ministry of Human Resource and Development”, India for the financial support to carry out the above work.
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Agrawal, P.N., Acu, A.M. & Sidharth, M. Approximation degree of a Kantorovich variant of Stancu operators based on Polya–Eggenberger distribution. RACSAM 113, 137–156 (2019). https://doi.org/10.1007/s13398-017-0461-0
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DOI: https://doi.org/10.1007/s13398-017-0461-0
Keywords
- Pólya–Eggenberger distribution
- Lipschitz class function
- Ditzian–Totik modulus of smoothness
- Bounded variation