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