New modified Baskakov operators based on the inverse Pólya-Eggenberger distribution

Abstract

In the present article we introduce some modifications of the Baskakov operators in sense of the Lupaş operators based on the inverse Pólya-Eggenberger distribution. For these new modifications we derive some direct results concerning the uniform convergence and the asymptotic formula, as well as some quantitative type theorems.

General family of exponential operators

“…A lot of work has already been done on construction of bivariate form of various linear positive operators and analysis of their convergence results. We refer to the readers some interesting articles (see [1], [2], [4], [9], [5], [12], [17], [19], [23], [26], [31]) for more information. The bivariate extension of the operators (4) for (x, y) ∈ I 2 = [0, 1] × [0, 1] and λ 1 > 0,λ 2 > 0 is defined as follows:…”

On the preservation of functions with exponential growth by modified Ismail–May operators

“…In past years, there have been several modifications of operators to enhance their convergence and error estimation process (see previous studies 6‐8 ). In 2003, King 9 presented a sequence of linear positive operators which approximated each continuous function on [0, 1] while preserving the test function x 2 .…”

Integral modification of Beta-Apostol-Genocchi operators

“…(cf. [1,5,4,7,8,19]). We address the Durrmeyer form modification of the linear positive operators represented by (1) for every real valued continuous and bounded functions f on [0, ∞) as described in the following:…”