Approximation of Some Classes of Functions by Landau Type Operators

Abstract

This paper aims to highlight a class of integral linear and positive operators of Landau type which have affine functions as fixed points. We focus to reveal approximation properties both in $$L_p$$ spaces and in weighted $$L_p$$ spaces $$(1\le p<\infty )$$ . Also, we give an extension of the operators to approximate real-valued vector functions. In this case, the study pursues the approximation of continuous functions on convex compacts. The evaluation of the rate of convergence in one and multidimensional cases is performed by using adequate moduli of smoothness.