Quantitative-Voronovskaja-type theorems for novel generalized-Szasz-Durrmeyer operators incorporating the Sheffer sequences

In this work, a novel hybrid approximation operator based on a versatile generalization of the classic Szasz-Mirakjan operators, and incorporating the Sheffer sequences is considered. It is demonstrated how the proposed operators can get reduced to a multitude of operators involving classic approximation operators studied over past many decades. We call the individual cases generalized Bernstein, Baskakov, Lupas and Szasz-Mirakjan operators, each incorporating the Sheffer and Appell polynomials. Indispensable properties of the proposed operators based on first and second order modulus of continuity are derived. Approximation on weighted space is also studied. Further, quantitative Voronovskaja-type theorems have very recently been acknowledged as valuable approximation properties. These form a momentous part of the present work. We conclude with an explicit graphical demonstration of approximation by the proposed operators in the case of the Sheffer sequence reduced to the Bell polynomials.