Jain–Durrmeyer operators associated with the inverse Pólya–Eggenberger distribution

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.…”

Stancu Type Baskakov—Durrmeyer Operators and Approximation Properties

“…For α = 0, operators (9) are reduced to (5). For the operators based on (P-E) distribution, one can see the details in [12][13][14]. Gupta et al [15] introduced Durrmeyer type modification of (9) as follows:…”

Generalized Positive Linear Operators Based on PED and IPED

“…Very recently Durrmeyer type modification of generalized Baskakov operators (1.2) associated with IPED were introduced by Dhamija and Deo [6] and studied the moments with the help of Vandermonde convolution formula and then gave approximation properties of these operators which include uniform convergence and degree of approximation. Deo et al [4] also investigated approximation properties of Kantorovich variant of operators (1.2) and they established uniform convergence, asymptotic formula and degree of approximation.…”