In the present paper, we introduce the Durrmeyer variant of Baskakov-Bezier operators Bn,α(f, x), which is the modified form of Baskakov-Beta operators. Here we obtain an estimate on the rate of convergence of Bn,α(f, x) for functions of bounded variation in terms of Chanturiya’s modulus of variation. In the end we also propose an open problem for the readers.

In 1967 Durrmeyer introduced a modiication of the Bernstein polynomials as a selfadjoint polynomial operator on L 2 0; 1] which proved to be an interesting and rich object of investigation. Incorporating Jacobi weights Berens and Xu obtained a more general class of operators, sharing all the advantages of Durrmeyer's modiication, and identiied these operators as de la Vall ee{Poussin means with...

In this paper, we are dealing with Cheney-Sharma Chlodovsky Durrmeyer operators and studying their approximation properties. The Bohman-Korovkin theorem is verified estimated the convergence properties using of modulus continuity, Lipschitz- type space, Ditzian-Totik continuity. After that, weighted result also given. Finally, some results related to A-statistical o...

In this article, our main purpose is to define the p , q -variant of Szász-Durrmeyer type operators with help Dunkl generalization generated by an exponential function. We estimate moments and establish some direct results aforementioned operators. ...

In this paper, the order of simultaneous approximation and Voronovskaja type theorems with quantitative estimate for complex genuine q-Bernstein-Durrmeyer polynomials (0 < q < 1) attached to analytic functions on compact disks are obtained. Our results show that extension of the complex genuine q-Bernstein-Durrmeyer polynomials from real intervals to compact disks in the complex plane extends a...

We give a generalisation of the multivariate beta integral. This is used to show that the (multivariate) Bernstein–Durrmeyer operator for a Jacobi weight has a limit as the weight becomes singular. The limit is an operator previously studied by Goodman and Sharma. From the elementary proof given, it follows that this operator inherits many properties of the Bernstein–Durrmeyer operator in a nat...

Keywords: Baskakov–Durrmeyer operator Pointwise convergence Asymptotic formula q-Analogue a b s t r a c t In this paper, we are dealing with a new type of Baskakov–Durrmeyer–Stancu (BDS) operators D ða;bÞ n ðf ; xÞ defined by (1.4). First we estimate moments of these operators and also obtain the recurrence relations for the moments. We estimate some approximation properties and asymptotic form...

and Applied Analysis 3 Since 1967, Durrmeyer introduced Bernstein-Durrmeyer operators, and there are many paperswhich studied theirproperties 1–7 . In 1991, Zhang studied the characterization of convergence forMn,1 f ;x with Jacobi weights. In 1992, Zhou 5 considered multivariate Bernstein-Durrmeyer operators Mn,d f ;x and obtained a characterization of convergence. In 2002, Xuan et al. studied...

The main object of this paper is to construct a new Durrmeyer variant the ?-Bernstein type operators which have better features than classical one. Some results concerning rate convergence in terms first and second moduli continuity asymptotic formulas these are given. Moreover, we define bivariate case investigate approximation degree by means total partial modulus Peetre?s K-functional. A Vor...