We define GBS operators of Durrmeyer for bivariate functions on simplex and we give their approximations rate B-continuous B-differentiable functions. show that the type new have better approximation than operators.

Abstract In this article, we the study generalized family of positive linear operators based on two parameters, which are a broad many well-known operators, e.g., Baskakov-Durrmeyer, Baskakov-Szász, Szász-Beta, Lupa?-Beta, Lupa?-Szász, genuine Bernstein-Durrmeyer, and P?lt?nea. We first find direct estimates in terms second-order modulus continuity, then an estimate error Ditzian-Totik smoothne...

The present paper deals with the Szász-Mirakyan-Durrmeyer-Stancu operators preserving

The present article deals with the general family of summationintegral type operators. Here, we propose the Durrmeyer variant of the generalized Lupaş operators considered by Abel and Ivan (General Math. 15 (1) (2007) 21-34) and study local approximation, Voronovskaja type formula, global approximation, Lipchitz type space and weighted approximation results. Also, we discuss the rate of converg...

Abstract. We consider a class of positive linear operators which, among others, constitute a link between the classical Bernstein operators and the genuine Bernstein–Durrmeyer mappings. The focus is on their relation to certain Lagrange-type interpolators associated to them, a well known feature in the theory of Bernstein operators. Considerations concerning iterated Boolean sums and the deriva...

Keywords: Bernstein operators Pointwise approximation Rate of convergence a b s t r a c t In the present paper, we study pointwise approximation by Bernstein–Durrmeyer type operators in the mobile interval x 2 0; 1 À 1 nþ1 h i , with use of Peetre's K-functional and x 2 u k ðf ; tÞ ð0 6 k 6 1Þ, we give its properties and obtain the direct and inverse theorems for these operators.

Khan [4] and Mishra [5] have proved some results dealing with the degree of approximation of functions in Lpspaces using different types of operators. BaskakovDurrmeyer operators were first considered by Sahai-Prasad [8] in 1985 . Sinha et al. [9] improved and corrected the results of [8]. In 2005, Finta [1], introduced a new type of Baskakov-Durrmeyer operator by taking the weight function of ...

*Correspondence: [email protected] College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050024, People’s Republic of China Hebei Key Laboratory of Computational Mathematics and Applications, Shijiazhuang, 050024, People’s Republic of China Abstract We give the direct and inverse approximation theorems for a new type of Bernstein-Durrmeyer operators with the mod...

In the present paper, we introduce genuine q-Stancu-Bernstein–Durrmeyer operators Znq,α(f;x). We calculate moments of these operators, Znq,α(tj;x) for j=0,1,2, which follows a symmetric pattern. also second order central moment Znq,α((t−x)2;x). give Korovkin-type theorem; estimate rate convergence continuous functions. Furthermore, prove local approximation theorem in terms modulus continuity; ...