A new type of convergence in partial metric spaces
DOI:
https://doi.org/10.62918/hjma.v3i2.31Keywords:
Partial metric space, deferred mean, statistical convergence, deferred statistical convergenceAbstract
In this paper, we introduce the concept of deferred statistical convergence in partial metric spaces (pms), extending classical notions of statistical convergence and summability. We define deferred Cesaro summability and investigate its fundamental properties. Connections between statistical convergence and deferred Cesaro summability are explored, including inclusion relationships and strictness. Additionally, we establish conditions under which deferred summability implies statistical convergence and vice versa. Examples and theorems are provided to illustrate the applicability and relevance of these concepts in partial metric spaces.
References
R. P. Agnew, On deferred Cesaro mean, Ann. Math. 33 (1932) 413--421.
J. S. Connor, The Statistical and strong p-Cesaro convergence of sequences, Analysis 8 (1988) 47--63.
M. Et, M. Cinar, H. Sengul, On deferred statistical convergence in metric spaces, Conference Proceedings of Science and Technology 2(3) (2019) 189--193.
H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951) 241--244.
A. Fridy, On statistical convergence, Analysis 5 (1985) 301--313.
S. Gupta, V. K. Bhardwaj, On deferred f-statistical convergence, Kyungpook Math. J. 58 (1) (2018) 91--103.
M. Kucukaslan, M. Yılmazurk, On deferred statistical convergence of sequences, Kyungpook Math. J. 56} (2016) 357--366.
S. G. Matthews, Partial metric topology, Ann. New York Acad. Sci. 728 (1994) 183--197.
F. Nuray, lambda-strongly summable and lambda-statistically convergent functions, Iran. J. Sci. Technol. Trans. A Sci. 34 (2010) 335--338.
F. Nuray, Statistical convergence in partial metric spaces, Korean J. Math. 30(1) (2022) 155--160.
T. Salat, On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980) 139--150.
I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959) 361--375.
H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951) 73--74.
A. Zygmund, Trigonometric series, Cambridge University Press, Cambridge, London and New York, 1979.
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Hilbert Journal of Mathematical Analysis is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.