Note on the $q$-Stancu-Schurer operator

Abstract

In this paper, we introduce a generalization of the Stancu-Schurer operators based on q-integers and get a Bohman-Korovkin type approximation theorem of these operators. We also compute the rate of convergence by using the first modulus of smoothness and give some numerical result of operators based on Matlab algorithms.

On the generalized Boolean sum Schurer-Stancu approximation formula

“…first considered by E. Dobrescu and I. Matei [7]. For other related results see [1], [10], [11], [12], [13], [14], [15], [16], [17], [21], [23], [26], [27], [28], [29], [32] and [39].…”

Some approximation properties of a Durrmeyer variant of q‐Bernstein–Schurer operators

“…The goal of this paper is to present approximation theorems for a Durrmeyer variant of q-Bernstein-Schurer operators defined by C.V. Muraru in [22] and modified by M.Y. Ren and X.M.…”

“…Zeng in [23]. C.V. Muraru and A.M. Acu in [24] studied the Durrmeyer variant of the q-Bernstein-Schurer defined in [22] using uniform convergence. Our choice is to use both the uniform convergence and the statistical convergence to establish some approximation theorems for the Durrmeyer variant of the modified q-Bernstein-Schurer operators.…”

“…Let p 2 N be fixed. For any m 2 N, f 2 COE0, pC1, the class of generalized q-Bernstein-Schurer operators is constructed in [22] as follows:…”

Note on a $q$-analogue of Stancu-Kantorovich operators

“…The goal of the present paper is to introduce a Kantorovich variant of q-Stancu operators and investigate their approximation properties. Many generalizations and applications of the Stancu operators were considered in the last years ( [1,2,11,15]).…”