On genuine Lupa\c{s}-Beta operators and modulus of continuity

Gupta, Vijay; Rassias, Th.M.; Pandey, Ekta

doi:10.22075/ijnaa.2017.10557.1508

On genuine Lupa\c{s}-Beta operators and modulus of continuity

Document Type : Research Paper

Authors

Vijay Gupta ¹

Th.M. Rassias ²

Ekta Pandey ³

¹ Netaji Subhas Institute of Technology New Delhi, India

² Department of Mathematics, National Technical University of Athens, Zofrafou Campus, 15780 Athens, Greece

³ Department of Mathematics, IMS Engineering College Ghaziabad-201009, (UP), India

10.22075/ijnaa.2017.10557.1508

Abstract

In the present article we discuss approximation properties of genuine Lupa\c{s}-Beta operators of integral type. We establish quantitative asymptotic formulae and a direct estimate in terms of Ditzian-Totik modulus of continuity. Finally we mention results on the weighted modulus of continuity for the genuine operators.

Keywords

factorial polynomials

Beta basis function

direct estimates

weighted modulus of continuity

$K$-functionals