TY  - JOUR
T1  - Deferred statistical order convergence in Riesz spaces
AU  - Aydın, Abdullah
AU  - Küçükaslan, Mehmet
PY  - 2024
DA  - October
DO  - 10.15672/hujms.1322652
JF  - Hacettepe Journal of Mathematics and Statistics
PB  - Hacettepe University
WT  - DergiPark
SN  - 2651-477X
SP  - 1368
EP  - 1377
VL  - 53
IS  - 5
LA  - en
AB  - In recent years, researchers have focused on exploring different forms of statistical convergence in Riesz spaces, such as statistical order convergence and statistical unbounded order convergence. This study aims to present the concept of deferred statistical convergence within Riesz spaces, specifically concerning its relationship with order convergence. Furthermore, we delve into the interconnections between deferred statistical order convergence and various other types of statistical convergence. Moreover, we explore in depth the intricate connections between deferred statistical order convergence and other notable forms of statistical convergence. We provide valuable insights into the broader framework of statistical convergence theory in Riesz spaces.
KW  - Riesz space
KW  - deferred statistical convergence
KW  - order convergence
KW  - deferred statistical order convergence
CR  - [1] R.P. Agnew, On deferred Cesàro means, Anna. Math. 33 (3), 413-421, 1932.
CR  - [2] C.D. Aliprantis and O. Burkinshaw, Locally Solid Riesz Spaces with Applications to
Economics, Mathematical Surveys and Monographs Centrum, 2003.
CR  - [3] C.D. Aliprantis and O. Burkinshaw, Positive Operators, Springer, Dordrecht, 2006.
CR  - [4] A. Aydın, Multiplicative order convergence in f-algebras, Hacet. J. Math. Stat. 49
(3), 998-1005, 2020.
CR  - [5] A. Aydın, The statistically unbounded $\tau$-convergence on locally solid vector lattices,
Turk. J. Math. 44 (3), 949-956, 2020.
CR  - [6] A. Aydın, The statistical multiplicative order convergence in vector lattice algebras,
Fact. Univ. Ser.: Math. Infor. 36 (2), 409-417, 2021.
CR  - [7] A. Aydın, M. Et, Statistically multiplicative convergence on locally solid Riesz algebras,
Turk. J. Math. 45 (4), 1506-1516, 2021.
CR  - [8] A. Aydın, E. Emelyanov and S. G. Gorokhova, Full lattice convergence on Riesz
spaces, Indagat. Math. 32 (3), 658-690, 2021.
CR  - [9] Z. Ercan, A characterization of u-uniformly completeness of Riesz spaces in terms of
statistical u-uniformly pre-completeness, Demons. Math. 42 (2), 383-387, 2009.
CR  - [10] M. Et, P. Baliarsingh, H. . Kandemir and M. Küçükaslan, On $\mu$-deferred statistical
convergence and strongly deferred summable functions, Rev. R. Acad. Cienc. Exactas
Fís. Nat. Ser. A Mat. 115(1), Paper No. 34, 14 pp, 2021.
CR  - [11] M. Et, M. Cinar and H. S. Kandemir, Deferred statistical convergence of order α in
metric spaces, AIMS Math. 5, Paper No. 4, 3731-3740, 2020.
CR  - [12] H. Fast, Sur la convergence statistique, Colloq. Math. 2, 241-244, 1951.
CR  - [13] J. Fridy, On statistical convergence, Analysis 5 (4), 301-313, 1985.
CR  - [14] M. Küçükaslan and M. Yilmazturk, On deferred statistical convergence of sequences,
Kyung. Math. J. 56 (2), 357-366, 2016.
CR  - [15] M. Küçükaslan, U. Deer and U. Dovgoshey, On statistical convergence of metric
valued sequences, Ukrain. Math. J. 66 (5), 796-805, 2014.
CR  - [16] W.A.J. Luxemburg and A.C. Zaanen, Vector Lattices I, North-Holland Pub. Co.,
Amsterdam, 1971.
CR  - [17] I.J. Maddox, Statistical convergence in a locally convex space, Math. Proc. Cambr.
Phil. Soc. 104 (1), 141-145, 1988.
CR  - [18] F. Riesz, Sur la Décomposition des Opérations Fonctionelles Linéaires. Bologna, Atti
Del Congresso Internazionale Dei Mathematics Press, 1928.
CR  - [19] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq.
Math. 2, 73-74, 1951.
CR  - [20] B.C. Tripathy, On statistically convergent sequences, Bul. Calcut. Math. Soc. 90,
259262, 1998.
CR  - [21] A.C. Zaanen, Riesz Spaces II, North-Holland Publishing C., Amsterdam, 1983.
UR  - https://doi.org/10.15672/hujms.1322652
L1  - https://dergipark.org.tr/en/download/article-file/3243682
ER  -