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Summer 2019 Generalized almost convergence of double sequences in modular function spaces
Ŭgur Kadak
Adv. Oper. Theory 4(3): 556-573 (Summer 2019). DOI: 10.15352/aot.1808-1412

Abstract

‎‎‎‎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.

Citation

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Ŭgur Kadak. "Generalized almost convergence of double sequences in modular function spaces." Adv. Oper. Theory 4 (3) 556 - 573, Summer 2019. https://doi.org/10.15352/aot.1808-1412

Information

Received: 29 August 2018; Accepted: 18 November 2018; Published: Summer 2019
First available in Project Euclid: 2 March 2019

zbMATH: 07056785
MathSciNet: MR3919031
Digital Object Identifier: 10.15352/aot.1808-1412

Subjects:
Primary: 40A30
Secondary: 39A70 , ‎40G15‎ , 46E30

Keywords: ‎almost convergence‎ , ‎bivariate Chlodowsky-Szász-Kantorovich-Charlier-type operator‎ , ‎fractional-order difference operator , Korovkin-type approximation theorem , ‎modular function space

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.4 • No. 3 • Summer 2019
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