in the present article, we propose the $(p,q)$variant of genuine baskakov durrmeyer operators. we obtain moments and establish some directresults, which include weighted approximation and results in terms of modulus of continuity of second order.

This paper deals with Stancu type generalization of q -analogue of Baskakov-Szasz operators introducing a new sequence of positive q -integral operators. We show that it is a weighted approximation process in the polynomial space of continuous functions defined on [0,∞). An estimate for the rate of convergence and weighted approximation properties are also obtained for these operators. MSC: 41A...

In the present paper we prove direct approximation theorems for discrete type operators (Lnf)(x) = ∞ ∑ k=0 un,k(x)λn,k(f), f ∈ C[0,∞), x ∈ [0,∞) using a modified K−functional. As applications we give direct theorems for Baskakov type operators, Szász-Mirakjan type operators and Lupaş operator.

In 1988, Felten obtained local and global approximation theorems for positive linear operators. In the last decade, Finta studied direct local and global approximation theorems for Baskakov type operators and SzaszMirakian type operators. In the present paper, we establish some local approximation estimates for a new family of beta operators, by using Ditzian-Totik modulus of smoothness.

In the present paper, we prove a global direct theorem for the modified Baskakov type operators in terms of so called DitzianTotik modulus of smoothness.

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.

Suppose that (Lm)m≥1 is a given sequence of linear and positive operators. Starting with the mentioned sequence, the new sequence (Km)m≥1 of linear and positive operators is constructed. For the operators (Km)m≥1 a convergence theorem and a Voronovskaja-type theorem are established. As particular cases of the general construction, we refined the Bernstein’s operators, the Stancu’s operators, th...

In the present article, we propose the $(p,q)$ variant of genuine Baskakov Durrmeyer operators. We obtain moments and establish some direct results, which include weighted approximation and results in terms of modulus of continuity of second order.

This paper is a study of the degree of approximation by the linear combinations of the derivatives of certain Durrmeyer type integral modification of the Baskakov operators in terms of the higher order modulus of smoothness.