Semi Post–Widder Operators and Difference Estimates

Abstract

We consider the Post–Widder operators of semi-exponential type, which are a generalization of the exponential operators connected with x^2. This modification has the beauty to find difference with other operators, while the original Post–Widder operators do not have such property. We estimate quantitative difference of these operators with Baskakov type operators and Szász–Kantorovich operators, along with some composition of operators. Finally, we further consider a form preserving linear functions and estimate some direct results.