Korovkin type theorem and iterates of certain positive linear operators

In this paper we prove Korovkin type theorem for iterates of general positive linear operators $T:C\left[ 0,1\right] \rightarrow C\left[ 0,1\right]$ and derive quantitative estimates in terms of modulus of smoothness. In particular, we show that under some natural conditions the iterates $T^{m}:C\left[ 0,1\right] \rightarrow C\left[ 0,1\right]$ converges strongly to a fixed point of the original operator $T$. The results can be applied to several well-known operators; we present here the $q$-MKZ operators, the $q$-Stancu operators, the genuine $q$-Bernstein--Durrmeyer operators and the Cesaro operators

Approximation properties of (p,q)-Meyer-Konig-Zeller Durrmeyer operators

In this paper, we introduce Durrmeyer type modification of Meyer-Konig-Zeller operators based on (p,q)-integers. Rate of convergence of these operators are explored with the help of Korovkin type theorems. We establish some direct results for proposed operators. We also obtain statistical approximation properties of operators. In last section, we show rate of convergence of (p,q)-Meyer-Konig-Zeller Durrmeyer operators for some functions by means of Matlab programming

Rate of approximation by new variants of Bernstein-Durrmeyer operators

In this paper, we give direct theorems on point wise and global approximation by new variants of Bernstein-Durrmeyer operator, introduced by A.-M. et al.[1].Comment: 21 page

B\'{e}zier Variant of generalized Bernstein-Durrmeyer type operators

In this paper, we define B\'{e}zier variant of generalized Bernstein-Durrmeyer type operators of second order, introduced by Ana et al. Then, we find an error estimate in terms of terms of Ditzian Totik modulus of smoothness. Next, we study the rate of approximation for a larger class of functions of bounded variation.Comment: 12 pages. arXiv admin note: substantial text overlap with arXiv:2005.0388

On Simultaneous Approximation of Modified Baskakov Durrmeyer Operators

In this present manuscript, we discuss properties of modified Baskakov-Durrmeyer-Stancu (BDS) operators with parameter $\gamma>0$. We compute the moments of these modified operators. Also, establish point-wise convergence, Voronovskaja type asymptotic formula and an error estimation in terms of second order modification of continuity of the function for the operators $B_{n,\gamma}^{\alpha,\beta}(f,x)$.Comment: 14 pages, International Journal of Analysis,201

Approximation by Complex Baskakov-Szasz-Durrmeyer Operators in Compact Disks

In this paper, we deal with the complex Baskakov-Szasz-Durrmeyer mixed operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth in the open disk of radius R. Also, the exact order of approximation is found. The method used allows to construct complex Szasz-type and Baskakov-type approximation operators without involving the values on the positive real axis

A Nice Representation for a Link between Baskakov- and Sz\'asz-Mirakjan-Durrmeyer Operators and their Kantorovich Variants

In this paper we consider a link between Baskakov-Durrmeyer type operators and corresponding Kantorovich type modifications of their classical variants. We prove a useful representation for Kantorovich variants of arbitrary order which leads to a simple proof of convexity properties for the linking operators. This also solves an open problem. Another open problem is presented at the end of the paper

Rate of convergence of certain families of Jain operators of integral type

In the present paper, the authors introduce and investigate new sequences of positive linear operators which include some well known operators as special cases. Here we estimate the rate of convergence for functions having derivatives of bounded variation by families of Jain operators of integral type

Moment Estimations of new Sz\'asz-Mirakyan-Durrmeyer operators

In [10] Jain introduced the modified form of the Sz\'asz-Mirakjan operator, based on certain parameter $0\le\beta<1$. Several modifications of the operators are available in the literature. Here we consider actual Durrmeyer variant of the operators due to [10]. It is observed here that the Durrmeyer variant has the nice properties and one need not to take any restriction on $\beta$ in order to get convergence. We establish moments using the Tricomi's confluent hypergeometric function and Stirling numbers of first kind, also estimate some direct resultsComment: corrected typo

Approximation by (p,q)-Baskakov-Beta operators

In the present paper, we consider $(p,q)$-analogue of the Baskakov-Beta operators and using it, we estimate some direct results on approximation. Also, we represent the convergence of these operators graphically using MATLAB