Rate of Approximation by Finite Iterates of $$q$$ q -Durrmeyer Operators

Abstract

In this paper, we give direct theorems on point wise and global approximation by new variants of Bernstein-Durrmeyer operator, introduced by A.-M. et al.[1]. 1 0 p n,k (t)f (t) dt

Local and global results for modified Szász–Mirakjan operators

“…Walczak [10] discussed direct results related to pointwise and uniform convergence of the operators (8) in exponential weight spaces. Some more study in this area of approximation theory can be found in the References [11][12][13][14][15][16][17][18][19][20][21].…”

Some approximation properties of a new class of linear operators

“…The generalized Jain operators as variant of the Lupaş operators were studied by Patel and Mishra . Some related work in this area can be found in other works . Motivated by this, we give further modification of Jain operators in this paper with the help of a generalized Poisson‐type distribution, establish its convergence properties, and discuss its degree of approximation, asymptotic formula, and statistical convergence.…”

“…15 Some related work in this area can be found in other works. [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] Motivated by this, we give further modification of Jain operators in this paper with the help of a generalized Poisson-type distribution, establish its convergence properties, and discuss its degree of approximation, asymptotic formula, and statistical convergence. The results for the Szász-Mirakyan operators and Jain operators can be obtained from our operators as a particular case.…”

Approximation by Bivariate (p, q)-Bernstein–Kantorovich Operators

“…Very recently the well-known sequences of linear positive operators of approximation theory have been transferred to (p, q)-calculus and the advantages of (p, q) analogues of them have been intensively investigated. For some recent works devoted to classical, q and (p, q)-operators, we can refer the readers to Acar (2015Acar ( , 2016, Acar and Aral (2015), Gairola et al (2016), Mishra et al (2013a, b), Mishra and Pandey (2016), Mursaleen et al (2015a, b, c).…”