Advances in Difference Equations (Jan 2021)

A new construction of Lupaş operators and its approximation properties

  • Mohd Qasim,
  • Asif Khan,
  • Zaheer Abbas,
  • Qing-Bo Cai

DOI
https://doi.org/10.1186/s13662-020-03143-5
Journal volume & issue
Vol. 2021, no. 1
pp. 1 – 14

Abstract

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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