*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 a q -analogue of the bivariate Durrmeyer operators. A convergence theorem for these operators is established and the rate of convergence in terms of modulus of continuity is determined. Also, a Voronovskaja type theorem has been investigated for these operators. Mathematics subject classification (2010): 41A10, 41A36.

In this article, we consider Jain-Durrmeyer operators associated with the Apostol-Genocchi polynomials and study approximation properties of these Durrmeyer operators. Furthermore, examine behaviour including K-functional. We estimate rate convergence proposed for function in Lipschitz-type space local results by using modulus continuity. Employing Mathematica software, to show absolute error g...

Deo [5] introduced n-th Durrmeyer operators defined for functions integrable in some interval I. There are gaps and mistakes in some of his lemmas and theorems. Further, in his paper [4] he did not give results on simultaneous approximation as the title reveals. The purpose of this paper is to correct those mistakes. AMS subject classifications: 41A25, 41A30

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...

is the Baskakov basis function. Note that (1.1) is well defined, for n ≥ r +2, provided that f(t) = O(tr ) as t → ∞. The operators (1.1) were first introduced by Sahai and Prasad [9]. They termed these operators as modified Lupaş operators. In 1991, Sinha et al. [10] improved and corrected the results of [9] and denoted Ṽn as modified Baskakov operators. The rate of convergence of the operators...

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

In [10], for continuous functions f from the domain of certain discrete operators Ln the inequalities are proved concerning the modulus of continuity of Lnf . Here we present analogues of the results obtained for the Durrmeyer-type modification ̃ Ln of Ln. Moreover, we give the estimates of the rate of convergence of ̃ Lnf in Hölder-type norms

In this paper we will demonstrate a Voronovskajatype theorems and approximation theorems for GBS operators associated to some linear positive operators. Through particular cases, we obtain statements verified by the GBS operators of Bernstein, Schurer, Durrmeyer, Kantorovich, Stancu, BleimannButzer-Hahn, Mirakjan-Favard-Szász, Baskakov, Meyer-König and Zeller, Ismail-May.