Convergence of Integral Operators Based on Different Distributions

Abstract

We propose a new sequence of integral type operators, which is based on Polya and the binomial distributions. Here we have considered the value of $f(0)$ explicitly. It is observed that such integral operators preserve only the constant functions. We establish some direct results for the new sequence of linear positive operators. In the last section, we propose the modified form and observe that the modified form provides better approximation in the compact interval $\left[\frac{1}{3},\frac{1}{2}\right].$