On generalized integral Bernstein operators based on q-integers

On new class of linear and positive operators

“…The Durrmeyer type modification of Bernstein operators, Baskakov operators and Szász-Mirakyan operators are studied in [23][24][25][26][27][28][29]. Motivated by such type of operators, we generalize the operators L…”

Approximation by Kantorovich Type q-Bernstein-Stancu Operators

“…Later, Phillips [24] proposed other q-analog of Bernstein polynomials which became very popular and several researchers obtained the interesting approximation properties for q-Bernstein polynomials. In the recent years, many researchers have studied the approximation properties for linear positive operators [1,3,7,8,15,16,17,20,18]. Mursaleen et al in [22,23,19,21] have also obtained statistical approximation properties for new positive linear operators and some approximation theorems for generalized q-Bernstein-Schurer operators.…”

The voronovskaja type asymptotic formula for q-derivative of integral generalization of q-bernstein operators

“…Remark 1 ( [7]). For all m 2 N [ f0g; 0 , we have the following recursive relation for the images of the monomials t m under D ; n;q in terms of D n;q ; j = 0; 1; 2; : : : ; m, as…”

“…In 2014, Mishra and Patel [6,7] introduced the generalization due to Stancu THE VORONOVSKAJA TYPE ASYM PTOTIC FORM ULA 299 and proved Voronovskaja type asymptotic formula and various other approximation properties of the q-Durrmeyer-Stancu operators. Here, in this manuscript, we establish Voronovskaja type asymptotic formula for function having q-derivative.…”