Higher order Lupaş-Kantorovich operators and finite differences

Abstract

It is well-known that Lupas operators are not exponential type operators, although they preserve linear functions. The differential operator is not applicable to estimate nice representation between Lupas operators and its Kantorovich variant. In the present paper we use finite difference method viz. backward differences to estimate the recurrence relation for moments of the Lupas operators. We introduce higher order Lupas-Kantorovich operators and estimate some direct results.