Generalization of Szász operators: quantitative estimate and bounded variation

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Authors

  • K. Bozkurt National Defense University, Turkish Military Academy, Devlet Mah. Kara Harp Okulu Cd., 06420 Çankaya, Ankara, Turkey
  • M.L. Limmam Kirikkale University, 71450, Yahsihan, Kirikkale, Turkey
  • A. Aral Kirikkale University, 71450, Yahsihan, Kirikkale, Turkey https://orcid.org/0000-0001-9714-4729

DOI:

https://doi.org/10.15330/cmp.13.3.775-789

Keywords:

exponential Szász operator, exponential Szász-Kantorovich operator, convergence in variation

Abstract

Difference of exponential type Szász and Szász-Kantorovich operators is obtained. Similar estimates are given for higher order $\mu$-derivatives of the Szász operators and the Szász-Kantorovich type operators acting on the same order $\mu$-derivative of the function. These differences are given in quantitative form using the first modulus of continuity. Convergence in variation of the operators in the space of functions with bounded variation with respect to the variation seminorm is obtained. The results propose a general framework covering the results provided by previous literature.

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Published

2021-12-30

How to Cite

(1)
Bozkurt, K.; Limmam, M.; Aral, A. Generalization of Szász Operators: Quantitative Estimate and Bounded Variation: Array. Carpathian Math. Publ. 2021, 13, 775-789.

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Scientific articles