Boundedness of a Kantorovich type of the Szász-Mirakjan Operator

Abstract

Let Bn f represent the n-th Bernstein polynomial for f for each n ϵ ℕ and f ϵ C ([0, 1]) . Then for any f ϵ C ([0, 1]), the sequence {Bn f} converges uniformly to f. The generalisation of Bernstein polynomials to approximate functions defined on closed intervals [a, b] is straightforward. However, for functions with discontinuities, the convergence may fail. Kantorovich type of Szász-Mirakjan operator, S n f, enables us to approximate integrable functions on half space [0, ∞). In this paper, we show the boundedness of the Szász operators in Lp ([0, ∞)) , 1 ≤ p ≤ ∞.