Modified sampling Kantorovich operators in weighted spaces of functions

Abstract

This paper is devoted to construct a new modification of sampling Kantorovich operators. We introduce modified sampling Kantorovich operators by considering a special function $\rho$ that satisfies certain assumptions. We obtain pointwise and uniform convergence theorems in both continuous functions space and weighted spaces of continuous functions. We also give rate of convergence via weighted modulus of continuity in weighted spaces of continuous functions. In the last section, we present some examples of $\rho$-kernels which satisfies the corresponding assumptions. Finally, we give some graphical and numerical representations by comparing modified sampling Kantorovich operators and the classical sampling Kantorovich operators.