Parametric generalization of the q-Meyer-Krnig-Zeller operators

Abstract

In this paper, we introduce alpha parametric generalization of the Meyer-Konig-Zeller operators based on q-integer, which provides better error estimation then the usual q-MKZ operators. We obtain a differential recurrence relation satisfied by (alpha, q)-Meyer-Konig and Zeller operators and by using it, we calculate the moments (t/1-t)(m), m is an element of{0, 1, 2, 3, 4} more efficiently. We compute the error of approximation by means of the modulus of continuity and modified Lipschitz class functionals. We further derive the Riccati differential equation satisfied by the first three moments. Graphical and numerical illustrative examples are also given to show the power of approximation with these new operators. Finally, an illustrative real-world example associated with the surface air temperature been investigated to demonstrate the modeling capabilities of these operators.