On Modulated Lacunary Statistical Convergence of Double Sequences

María del Pilar Romero de la Rosa ()
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María del Pilar Romero de la Rosa: Department of Mathematics, University of Cádiz, Avda. de la Universidad s/n, 11405 Jerez de la Frontera, Cádiz, Spain

Mathematics, 2023, vol. 11, issue 4, 1-10

Abstract: In earlier works, F. León and coworkers discovered a remarkable structure between statistical convergence and strong Cesàro convergence, modulated by a function f (called a modulus function). Such nice structure pivots around the notion of compatible modulus function. In this paper, we will explore such a structure in the framework of lacunary statistical convergence for double sequences and discover that such structure remains true for lacunary compatible modulus functions . Thus, we continue the work of Hacer ?enül, Mikail Et and Yavuz Altin, and we fully solve some questions posed by them.

Keywords: double sequences; lacunary convergence; statistical convergence; strong Cesàro convergence; modulus function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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