Modular filter convergence theorems for Urysohn integral operators and applications

Boccuto, Antonıo; Dimitriou, Xenofon

doi:10.1007/s10114-013-1443-6

Cited by 16 publications

(8 citation statements)

References 9 publications

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“…This notion has been several applications in the very recent literature. Among them we recall weak ideal compactness in measure spaces (see also Boccuto, Das, Dimitriou, & Papanastassiou, 2012;Boccuto, Dimitriou, & Papanastassiou, 2010b;Dimitriou, 2011), Approximation Theory, signal sampling and reconstruction of images (see also Bardaro, Boccuto, Dimitriou, & Mantellini, 2012, 2013, 2013cDuman, 2007;Higgins & Stens, 1999), and in particular Brooks-Jewett, Dieudonné, Nikodým convergence and Vitali-Hahn-Saks-type theorems, with which we deal in this paper.…”

Section: Introductionmentioning

confidence: 99%

Ideal Limit Theorems and Their Equivalence in $(\ell)$-Group Setting

Boccuto¹,

Dimitriou²

2013

JMR

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We prove some equivalence results between limit theorems for sequences of ( )-group-valued measures, with respect to order ideal convergence. A fundamental role is played by the tool of uniform ideal exhaustiveness of a measure sequence already introduced for the real case or more generally for the Banach space case in our recent papers, to get some results on uniform strong boundedness and uniform countable additivity. We consider both the case in which strong boundedness, countable additivity and the related concepts are formulated with respect to a common order sequence and the context in which these notions are given in a classical like setting, that is not necessarily with respect to a same (O)-sequence. We show that, in general, uniform ideal exhaustiveness cannot be omitted. Finally we pose some open problems.

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Section: Introductionmentioning

confidence: 99%

Ideal Limit Theorems and Their Equivalence in $(\ell)$-Group Setting

Boccuto¹,

Dimitriou²

2013

JMR

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“…coincides with L ̺ (I). The notions about modulars have been introduced in [19] and have been widely discussed in [4], [5], [7], [9]- [11], [13], [14], [16]- [18], and [20].…”

Section: Introductionmentioning

confidence: 99%

Abstract Korovkin type theorems on modular spaces by $\mathscr{A}$-summability

Taş¹

2018

Math.Boh.

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Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://dml.cz 143 (2018) MATHEMATICA BOHEMICA No. 4, 419-430

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“…Recently some versions of Korovkin type theorems have been proved in modular spaces which include as particular cases L p , Orlicz and Musielak-Orlicz spaces [9,21]. Also more general convergences, for example convergences generated by summability methods, statistical, lter convergence, have also been used for the sequence of operators in order to correct the lack of convergence since it is well known that they provide a nonconvergent sequence to converge [6,10,12,15,16,17,22,23].…”

Section: Introductionmentioning

confidence: 99%