α-Schurer Durrmeyer operators and their approximation properties

Abstract

The key goal of the present research article is to introduce a new sequence of linear positive operator i.e., $\alpha$-Schurer Durrmeyer operator and their approximation behaviour on the basis of function $\eta(z)$, where $\eta$ infinitely differentiable on $[0,1]$, $\eta(z)=0$, $\eta(1)=1$ and $\eta'(z)>0$, for all $z\in[0,1]$. Further, we calculate central moments and basic estimates for the sequence of the operators. Moreover, we discuss the rate of convergence and order of approximation in terms of modulus of continuity, smoothness, Korovkin theorem, and Peeter's K-functional. Lastly, local and global approximation properties are studied in the subsequent section.