Approximation by quantum analogue of a new type of Szasz-Mirakjan-Kantorovich operators

In this work, we employ
q
-integers to develop the Kantorovich formula for novel Szász-Mirakjan operators and discuss their weighted approximation results. We look at the Ditzian-Totik modulus of continuity for these innovative operators to derive uniform global approximations. We compute the local direct estimate using Lipschitz-maximal functions as well as Peetre’s
K
-functional. Lastly, the Voronovskaja kind theorems are also demonstrated.

MSC: 41A25, 41A36