LACUNARY STATISTICAL CONVERGENCE OF ORDER α IN PARTIAL METRIC SPACES
Abstract
The present study introduces the notions of statistical convergence of order $\alpha$ and strongly $q-$ summability of order $\alpha$ in partial metric spaces. We examine
the inclusion relations linked to these these concepts.
Keywords
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N.D. Aral and H.S¸eng¨ul Kandemir: I−Lacunary statistical convergence of order β of difference sequences of fractional order, Facta Universitatis (NIS) Ser. Math. Inform., 36(1), (2021), 43-55.
N.D. Aral, H.S¸eng¨ul Kandemir and M. Et: Strongly lacunary convergence of order β of difference sequences of Fractional Order in Neutrosophic Normed Spaces, Filomat, 37(19), (2023), 6443-6451.
Y. Altın, H. Altınok and R. C¸olak: Statistical convergence of order α for difference sequences, Quaestiones Mathematicae, 38(4), (2015), 505-514. doi: 10.2989/16073606.2014.981685.
B. Bilalov and T. Nazarova: On statistical convergence in metric space, Journal of Mathematics Research, 7(1), (2015), 37-43. doi: 10.5539/jmr.v7n1p37.
R. C¸olak: Statistical convergence of order α, Modern Methods in Analysis and Its Applications, edited by M. Mursaleen, 121-129. New Delhi, India: Anamaya Publication, 2010.
R. C¸olak and C¸ .A. Bektas¸: λ-statistical convergence of order α, Acta Mathematica Scientia, 31(3), (2011), 953–959. doi: 10.1016/S0252-9602(11)60288-9.
M. Et and H. S¸eng¨ul: Some cesaro-type summability spaces of order α and lacunary statistical convergence of order α. Filomat 28(8), (2014), 1593-1602.
H. Fast: Sur la convergence statistique, Colloquium Mathematicae, 2, 3-4, (1951), 241-244. doi: 10.4064/cm-2-3-4-241-244.
J. A. Fridy and C. Orhan: Lacunary statistical convergence. Pacific Journal of Mathematics 160(1), (1993), 43-51.
J. A. Fridy and C. Orhan: Lacunary statistical summability. Journal
of Mathematical Analysis and Applications 173(2), (1993), 497-504.
doi.org/10.1006/jmaa.1993.1082
E. G¨ulle, E. D¨undar and U. Ulusu: Summability anad lacunary statistical convergence concepts in partial metric. Preprint, 2023. doi.org/10.1006/jmaa.1993.1082
S.G. Matthews: Partial metric topology, Annals of the New York Academy of Sciences, 728, (1994), 183-197. doi:10.1111/j.1749-6632.1994.tb44144.x.
F. Nuray: Statistical convergence in partial metric spaces, Korean Journal of Mathematics, 30(1), (2022), 155-160. doi: 10.11568/kjm.2022.30.1.155.
I. J. Schoenberg: The integrability of certain functions and related summability methods, The American Mathematical Monthly, 66, (1959), 361-375. doi:10.1080/00029890.1959.11989303.
H. S¸eng¨ul and M. Et: On lacunary statistical convergence of order α, Acta Mathematica Scientia, 34(2), (2014), 473-482. doi.org/10.1016/S0252-9602(14)60021-7
H. S¸eng¨ul and M. Et: On I− lacunary statistical convergence of order α of sequences of sets, Filomat, 31(8), (2017), 2403-2412.
H.S¸eng¨ul, M. Et and H. C¸ akallı: Lacunary d-statistical boundedness of order α in metric spaces. Azerbaijan Journal of Mathematics, 12(1), (2022), 98-108.
H. Steinhaus: Sur la convergence ordinaire et la convergence asymptotique, Colloquium Mathematicum, 2, (1951), 73-74.
A. Zygmund: Trigonometric Series, Cambridge: Cambridge University Press, 1979.
DOI: https://doi.org/10.22190/FUMI230517049B
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