Approximation Properties of a New (p,q)-Post-Widder Operator

We introduce a new (p,q)-Post-Widder operator along with its modified form which preserves the test functions xγ,γ∈N. This paper aims to investigate the approximation properties of the (p,q)-Post-Widder operator while preserving xγ. We estimate the convergence rate of the operators with the help of a continuity module and discuss their asymptotic behavior in terms of the weighted modulus of continuity. Also, our numerical results show that the new operator preserving x3 provides the best approximation. In addition, we establish quantitative estimates of the difference between the two kinds of (p,q)-Post-Widder operators. Finally, using numerical examples and graphs, we illustrate that, for particular cases, our results provide improved convergence estimates.