Article

# Convergence of the q analogue of Szász-Beta operators.

Kırıkkale University Faculty of Science and Arts, Department of Mathematics, Yahşihan, Kirikkale, Turkey

Applied Mathematics and Computation (Impact Factor: 1.6). 03/2010; 216:374-380. DOI: 10.1016/j.amc.2010.01.018 Source: DBLP

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**ABSTRACT:**We introduce a new kind of modification of Durrmeyer type q-Baskakov operators D n,q based on the concept of q-integral. These operators are different from those proposed by A. Aral and V. Gupta in [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 3-4, A, 1171–1180 (2010; Zbl 1180.41012)]. We establish direct and local approximation theorems of operators D n,q and obtain the estimates on the rate of convergence and weighted approximation of operators D n,q .Georgian Mathematical Journal 01/2012; 19(1). · 0.34 Impact Factor - Applied Mathematics and Computation 03/2014; 235:555-559. · 1.35 Impact Factor
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**ABSTRACT:**In the present paper, we introduce the q-analogue of the general Gamma type operators. We establish the moments of the operators by using the q-derivatives and then prove the basic convergence theorem. Next, the Voronovskaja type theorem and some direct results for the above operators are discussed. Also, the rate of convergence and weighted approximation by these operators in terms of modulus of continuity are studied. Then, we obtain point-wise estimate using the Lipschitz type maximal function. Further, we study the A-statistical convergence of these operators. Lastly, we propose a king type modi�cation of these operators to obtain better estimates.Applied Mathematics and Computation 12/2014; 251(Jan, 2015):564-575. · 1.60 Impact Factor

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## Vijay Gupta |