Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2014; 51(2): 303-315

Printed March 31, 2014

https://doi.org/10.4134/BKMS.2014.51.2.303

Copyright © The Korean Mathematical Society.

On a sequence of Kantorovich type operators via Riemann type $q$-integral

G\"ulen Ba\c{s}canbaz-Tunca, Ay\c{s}eg\"ul Eren\c{c}in, and Fatma Ta\c{s}delen

Ankara University, Abant izzet Baysal University, Ankara University

Abstract

In this work, we construct Kantorovich type generalization of a class of linear positive operators via Riemann type $q$-integral. We obtain estimations for the rate of convergence by means of modulus of continuity and the elements of Lipschitz class and also investigate weighted approximation properties.

Keywords: Kantorovich type operator, Riemann type $q$-integral, weighted spaces, modulus of continuity, Lipschitz class

MSC numbers: 41A25, 41A36