Abstract
In the present article we discuss direct estimates of the Durrmeyer type modifications of the well-known Szász-Mirakyan operators. The present article is divided into two sections. In the first section, we mention some of the different integral modifications of the Szász-Mirakyan operators and mention their direct results which were done in ordinary, and specially in the simultaneous approximation.
In the second section for the Szász-Mirakyan-Beta operators, we find the alternate hypergeometric representation and propose their Stancu type generalization based on two parameters. We obtain the moments using confluent Hypergeometric functions. Also it is observed here that the moments are related to the Laguerre polynomials. We study direct approximation results for these Szász-Mirakyan-Beta-Stancu operators, which include a Voronovskaja-type asymptotic formula and error estimations in terms of modulus of continuity.
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Govil, N.K., Gupta, V., Soybaş, D. (2014). Certain Szász-Mirakyan-Beta Operators. In: Rassias, T., Tóth, L. (eds) Topics in Mathematical Analysis and Applications. Springer Optimization and Its Applications, vol 94. Springer, Cham. https://doi.org/10.1007/978-3-319-06554-0_15
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