Advances in Operator Theory

Generalized almost convergence of double sequences in modular function spaces

Ŭgur Kadak

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‎‎‎‎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.

Article information

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 40A30: Convergence and divergence of series and sequences of functions
Secondary: 46E30‎ ‎40G15‎ ‎39A70

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


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.

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