Advances in Operator Theory
- Adv. Oper. Theory
- Volume 4, Number 3 (2019), 556-573.
Generalized almost convergence of double sequences in modular function spaces
This article deals with almost convergence of double sequences using a new generalization of fractional-order difference operator in modular spaces and application to the Korovkin-type approximation in the context of modular spaces for positive linear operators. We then obtain several inclusion relations and present some examples, include proper non-trivial extensions of the corresponding classical ones. Further, we extend our study to new modular forms of Korovkin-type approximation theorems. Finally, we give an example using bivariate Chlodowsky-Szász-Kantorovich-Charlier-type operators and outline possible further extensions and improvements, in order to illustrate the effectiveness of the proposed methods.
Adv. Oper. Theory, Volume 4, Number 3 (2019), 556-573.
Received: 29 August 2018
Accepted: 18 November 2018
First available in Project Euclid: 2 March 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 40A30: Convergence and divergence of series and sequences of functions
Secondary: 46E30 40G15 39A70
Kadak, Ŭgur. Generalized almost convergence of double sequences in modular function spaces. Adv. Oper. Theory 4 (2019), no. 3, 556--573. doi:10.15352/aot.1808-1412. https://projecteuclid.org/euclid.aot/1551495620