Properties of q-analogue of Beta operator

Abstract

In this article, we introduce the q-variant of Beta operator. We find the recurrence formula for mth-order moments. Here, we establish some direct theorems in terms of modulus of continuity for these operators. We also propose conditions for better approximation. In the end, we also propose the Stancu-type generalization. Mathematical Subject Classification: 41A25; 41A35.

On the Iterated Exponent of Convergence of Solutions of Linear Differential Equations with Entire and Meromorphic Coefficients

“…In this paper, we improve and extend the above results by considering the iterated order, and we obtain the following theorems. For some closely related to applications of this paper, see the papers of Gupta et al [7,8]. .…”

“…Assume that ̸ ≡ 0 is a meromorphic solution of (8). By (8) we get that the poles of ( can only occur at the poles of 0 , , ,…”

On Durrmeyer-type generalization of (p, q)-Bernstein operators

“…Bernstein polynomials, their Durrmeyer variants and Sźasz operators which are generalization of Bernstein polynomials have been studied intensively by many researchers; for details one may refer to [2][3][4][5][6][7]13,14,24,26]. Motivated by these operators, we introduce ( p, q)-Bernstein Durrmeyer operators for 0 < q < p ≤ 1, n ∈ N and f ∈ C[0, 1] as:…”

q-Durrmeyer operators based on Pólya distribution

“…Some other results and forms of qDurrmeyer type operators were discussed in [2,5,7,10,11] and [8] etc. We now introduce the q-analogue of Lupaş Durrmeyer operators for f ∈ C[0, 1] and 0 < q < 1 by…”