On Modulated Lacunary Statistical Convergence of Double Sequences

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...

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Bibliographic Details
Published inMathematics (Basel) Vol. 11; no. 4; p. 1042
Main Author de la Rosa, María
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.02.2023
Subjects
Convergence
Convergence (Mathematics)
double sequences
lacunary convergence
Mathematical research
modulus function
Sequences (Mathematics)
statistical convergence
strong Cesàro convergence
United States
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Summary: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 Şenül, Mikail Et and Yavuz Altin, and we fully solve some questions posed by them.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11041042