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In this article, we the study generalized family of positive linear operators based on two parameters, which are a broad family of many well-known linear positive operators, e.g., Baskakov-Durrmeyer, Baskakov-Szász, Szász-Beta, Lupaş-Beta, Lupaş-Szász, genuine Bernstein-Durrmeyer, and Pǎltǎnea. We first find direct estimates in terms of the second-order modulus of continuity, then we find an estimate of error in the Ditzian-Totik modulus of smoothness. Then we discuss the rate of approximation for functions in the Lipschitz class. Furthermore, we study the pointwise Grüss-Voronovskaja-type result and also establish the Grüss-Voronovskaja-type asymptotic formula in quantitative form.

In this paper, we introduce a modified Bernstein-type operators based on two real parameters and study its various approximation properties. We derive some direct results e.g. Voronovkaja type asymptotic theorem, an estimate of error in ordinary as well as in Ditzian Totik modulus of smoothness and an error estimate for functions belonging to the Lipschitz type space. Further, we examine the rate of approximation for a Kirov and Popova type generalization of these operators. [ABSTRACT FROM AUTHOR]

In the present article, we study a generalization of Szász operators by Gould-Hopper polynomials. First, we obtain an estimate of error of the rate of convergence by these operators in terms of first order and second order moduli of continuity. Then, we derive a Voronovkaya-type theorem for these operators. Lastly, we derive Grüss-Voronovskaya type approximation theorem and Grüss-Voronovskaya type asymptotic result in quantitative form. [ABSTRACT FROM AUTHOR]

In this paper, we define Bézier variant of generalized Bernstein-Durrmeyer type operators of second order, introduced by Ana et al. Then, we find error estimate in terms of terms of Ditzian Totik modulus of smoothness. Next, we study rate of approximation for larger class function of bounded variation. [ABSTRACT FROM AUTHOR]

We obtain global rates of approximation by qq-Durrmeyer operators Dn,q(f;x) for the functions in the class Lp([0,1]), 1 ≤ p ≤ ∞. First, rates of approximation in terms of the norms of f and f' and in terms of the ordinary modulus of smoothness are obtained. Subsequently, we obtain rates of approximation in terms of the generalized modulus of smoothness ωφ(f,δ). [ABSTRACT FROM AUTHOR]

The present paper is a study of Lp-- approximation in terms of higher order integral modulus of smoothness for an iterative combination due to Micchelli, of certain summation-integral type operators using the device of Steklov means. [ABSTRACT FROM AUTHOR]

It is known [12] that the order of approximation by the Post-Widder operators is, at best, O(n-1), however smooth the function may be. So, Rathore and Singh [10] considered the linear combinations introduced by Rathore [9] to improve the order of approximation by these operators. The aim of this paper is to improve the rate of convergence of Post-Widder operators by applying the iterative combination technique introduced by Micchelli [8] for Bernstein polynomials and study the degree of approximation. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to study some direct results in simultaneous approximation for a linear combination of Bernstein-Durrmeyer type polynomials. [ABSTRACT FROM AUTHOR]