KANTOROVICH-STANCU TYPE OPERATORS

Abstract

ABSTRACT. Considering two given real parameters α, β which satisfy the condition 0 ≤ α ≤ β, D.D. Stancu ([11]) constructed and studied the linear positive operators P (α,β) m: C([0, 1]) → C([0, 1]), defined for any f ∈ C([0, 1]) and any m ∈ N by P (α,β)) m∑ k + α m f (x) = pmk(x)f. m + β k=0 In this paper, we are dealing with the Kantorovich form of the above operators. We construct the linear positive operators K (α,β) m: L1([0, 1]) → C([0, 1]), defined for any f ∈ L1([0, 1]) and any m ∈ N by m∑ f (x) = (m + β + 1) f(s)ds K (α,β) m k=0 ∫ k+α+1 m+β+1 pm,k(x) k+α m+β+1 and we study some approximation properties of the sequence