Unbounded p-Convergence in Lattice-Normed Vector Lattices

A. Aydın; E. Emelyanov; N. Erkurşun-Özcan; M. Marabeh

doi:10.3103/S1055134419030027

Unbounded p-Convergence in Lattice-Normed Vector Lattices

A. Aydın
, E. Emelyanov
, N. Erkurşun-Özcan
, M. Marabeh

Fonksiyonlar Teorisi ve Fonksiyonel Analiz Anabilim Dalı

Mus Alparslan University
Middle East Technical University
Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences
Palestine Technical University, Kadoorie

Araştırma sonucu: Dergiye katkı › Makale › bilirkişi

14 Alıntılar (Scopus)

Özet

A net x_α in a lattice-normed vector lattice (X, p, E) is unbounded p-convergent to x ∈ X if p(| x_α− x| ∧ u) → o 0 for every u ∈ X₊. This convergence has been investigated recently for (X, p, E) = (X, |·|, X) under the name of uo-convergence, for (X, p, E) = (X, ‖·‖, ℝ) under the name of un-convergence, and also for (X, p, ℝ^X ^′) , where p(x)[f]:= |f|(|x|), under the name uaw-convergence. In this paper we study general properties of the unbounded p-convergence.

Orijinal dil	İngilizce
Sayfa (başlangıç-bitiş)	164-182
Sayfa sayısı	19
Dergi	Siberian Advances in Mathematics
Hacim	29
Basın numarası	3
DOI'lar	https://doi.org/10.3103/S1055134419030027
Yayın durumu	Yayınlandı - 1 Tem 2019

Belgeye Erişim

10.3103/S1055134419030027

Diger dosyalar ve linkler

Link to publication in Scopus

Bundan alıntı yap

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title = "Unbounded p-Convergence in Lattice-Normed Vector Lattices",

abstract = "A net xα in a lattice-normed vector lattice (X, p, E) is unbounded p-convergent to x ∈ X if p(| xα− x| ∧ u) → o 0 for every u ∈ X+. This convergence has been investigated recently for (X, p, E) = (X, |·|, X) under the name of uo-convergence, for (X, p, E) = (X, ‖·‖, ℝ) under the name of un-convergence, and also for (X, p, ℝX ′) , where p(x)[f]:= |f|(|x|), under the name uaw-convergence. In this paper we study general properties of the unbounded p-convergence.",

keywords = "lattice-normed vector lattice, mixed-normed space, un-convergence, uo-convergence, vector lattice",

author = "A. Aydın and E. Emelyanov and N. Erkur{\c s}un-{\"O}zcan and M. Marabeh",

note = "Publisher Copyright: {\textcopyright} 2019, Allerton Press, Inc.",

year = "2019",

month = jul,

day = "1",

doi = "10.3103/S1055134419030027",

language = "English",

volume = "29",

pages = "164--182",

journal = "Siberian Advances in Mathematics",

issn = "1055-1344",

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TY - JOUR

T1 - Unbounded p-Convergence in Lattice-Normed Vector Lattices

AU - Aydın, A.

AU - Emelyanov, E.

AU - Erkurşun-Özcan, N.

AU - Marabeh, M.

PY - 2019/7/1

Y1 - 2019/7/1

N2 - A net xα in a lattice-normed vector lattice (X, p, E) is unbounded p-convergent to x ∈ X if p(| xα− x| ∧ u) → o 0 for every u ∈ X+. This convergence has been investigated recently for (X, p, E) = (X, |·|, X) under the name of uo-convergence, for (X, p, E) = (X, ‖·‖, ℝ) under the name of un-convergence, and also for (X, p, ℝX ′) , where p(x)[f]:= |f|(|x|), under the name uaw-convergence. In this paper we study general properties of the unbounded p-convergence.

AB - A net xα in a lattice-normed vector lattice (X, p, E) is unbounded p-convergent to x ∈ X if p(| xα− x| ∧ u) → o 0 for every u ∈ X+. This convergence has been investigated recently for (X, p, E) = (X, |·|, X) under the name of uo-convergence, for (X, p, E) = (X, ‖·‖, ℝ) under the name of un-convergence, and also for (X, p, ℝX ′) , where p(x)[f]:= |f|(|x|), under the name uaw-convergence. In this paper we study general properties of the unbounded p-convergence.

KW - lattice-normed vector lattice

KW - mixed-normed space

KW - un-convergence

KW - uo-convergence

KW - vector lattice

UR - https://www.scopus.com/pages/publications/85071622536

U2 - 10.3103/S1055134419030027

DO - 10.3103/S1055134419030027

M3 - Article

AN - SCOPUS:85071622536

SN - 1055-1344

VL - 29

SP - 164

EP - 182

JO - Siberian Advances in Mathematics

JF - Siberian Advances in Mathematics

IS - 3

ER -

Unbounded p-Convergence in Lattice-Normed Vector Lattices

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