Neutrosophic $ \mathfrak{Y} $-Cesàro summability of a sequence of order α of neutrosophic random variables in probability

Carlos Granados, Bright O. Osu, Birojit Das

Abstract


In this paper, we define the notions of neutrosophic $\mathfrak{Y}$-Cesàro summability of a sequence of order $\alpha$, neutrosophic $ \mathfrak{Y} $-lacunary statistical convergence of order $ \alpha $, neutrosophic strongly $ \mathfrak{Y} $-lacunary statistical convergence of order $ \alpha $ and neutrosophic strongly $ \mathfrak{Y} $-Ces\`aro summability of order $ \alpha $ in neutrosophic probability. Besides, we prove some relations among them.

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References


V.K. Rohatgi, An Introduction to Probability Theory and Mathematical Statistics. Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, New York, 1976. DOI: 10.1002/bimj.4710210813

S.K. Ghosal, Statistical convergence of a sequence of random variables and limit function, Applications of Mathematics 58 (2013), no. 4, 423–437.

F. Smarandache, Neutrosophic Probability, Set, and Logic (first version), In: F. Smarandache: Collected Papers, vol. III, Editura Abaddaba, Oradea, Romania, 2000.

F. Smarandache, A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability, American Research Press, Rehoboth, NM, 1999.

H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951), 73–74.

H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244.

M. Bisher, A. Hatip, Neutrosophic Random variables, Neutrosophic Sets and Systems 39 (2021), 45–52. DOI: 10.5281/zenodo.4444987

C. Granados, New notions on neutrosophic random variables, Neutrosophic Sets and Systems 47 (2021), 286–297. DOI: 10.5281/zenodo.5775135

C. Granados, J. Sanabria, On independence neutrosophic random variables, Neutrosophic Sets and Systems 47 (2021), 541–557. DOI: 10.5281/zenodo.5775184

C. Granados, A.K. Das, B. Das, Some Continuous Neutrosophic Distributions with Neutrosophic Parameters Based on Neutrosophic Random Variables, Advances in the Theory of Nonlinear Analysis and its Applications 6 (2022), no. 3, 380–389. DOI: 10.31197/atnaa.1056480

C. Granados, Some discrete neutrosophic distributions with neutrosophic parameters based on neutrosophic random variables, Hacettepe Journal of Mathematics and Statistics 51 (2022), 1442–1457. DOI: 10.15672/hujms.1099081

C. Granados, Statistical convergence of a sequence of neutrosophic random variables. Iranian Journal of Fuzzy Systems, Submitted.

F. Smarandache, Introduction to Neutrosophic Measure, Neutrosophic Integral and Neutrosophic Probability, Editura Sitech, Craiova, Romania, 2013. DOI: 10.5281/zenodo.8843

M. Ali, F. Smarandache, M. Shabir, L. Vladareanu, Generalization of Neutrosophic Rings and Neutrosophic Fields, Neutrosophic Sets and Systems 5 (2014), 9–14. DOI: 10.5281/zenodo.30172

F. Smarandache, Neutrosophic Set a Generalization of the Intuitionistic Fuzzy Sets, Inter. J. Pure Appl. Math. 24 (2005), no. 3, 287–297.

K. Kuratowski, Topologie, Monografie Matematyczne, tom 3, PWN-polish Scientific Publishers, Warszawa, 1933.

O. Kisi, E. Guler, I-Cesaro summability of a sequence of order α of random variables in probability, Fundamental Journal of Mathematics and Applications 1 (2018), no. 2, 157–161. DOI: 10.33401/fujma.480808




DOI: https://doi.org/10.52846/ami.v50i2.1718