Abstract

A central issue of the present paper is to consider the Korovkin-type approximation properties of the Lupaş-Jain operators using A-statistical convergence and Abel convergence, which are well-known summability methods. We provide an instance of a sequence of positive linear operators to which the weighted Korovkin-type theorem does not apply, but the A-statistical approximation theorem does. Our results are one-way more substantial than some approximation results given in [Başcanbaz-Tunca et al., On Lupaş-Jain Operators, Stud. Univ. Babeş-Bolyai Math., 63(4) (2018), 525--537].

Keywords: Lupaş-Jain operators; $A$-statistical convergence; Abel convergence; weighted spaces.

MSC: 41A25, 40A35, 41A36, 40G10, 40G15

DOI: 10.57016/MV-HRZW3917

Pages:  1--9