A new construction of Lupaş operators and its approximation properties

Abstract

Abstract The aim of this paper is to study a new generalization of Lupaş-type operators whose construction depends on a real-valued function ρ by using two sequences u m $u_{m} $ and v m $v_{m}$ of functions. We prove that the new operators provide better weighted uniform approximation over [ 0 , ∞ ) $[0,\infty )$ . In terms of weighted moduli of smoothness, we obtain degrees of approximation associated with the function ρ. Also, we prove Voronovskaya-type theorem, quantitative estimates for the local approximation.

Keywords

• Positive operators
• Voronovskaya-type theorem
• Weighted modulus of continuity
• Local approximation