α-Baskakov-Durrmeyer type operators and their approximation properties

In the present research article, we construct a new family of summation-integral type hybrid operators in terms of shape parameter alpha is an element of [0, 1]. Further, basic estimates, rate of convergence and the order of approximation with the aid of Korovkin theorem and modulus of smoothness are investigated. Moreover, numer4ical simulation and graphical approximations are studied. For these sequences of positive linear operators, we study the local approximation results using Peetre's K-functional, Lipschitz class and modulus of smoothness of second order. Next, we obtain the approximation results in weighted space. Lastly, A-statistical-approximation results are presented.