A Study on Lacunary Summability of Order α with respect to Modulus Function for Fuzzy Variables in Credibility Spaces


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Authors

Keywords:

Lacunary sequence, Lacunary Summability, Modulus Function, Fuzzy Variable Sequence, Credibility Space

Abstract

The main aim of this study is to investigate strongly lacunary summable and lacunary statistically convergent fuzzy variable sequences (briefly FVS) by utilizing modulus functions f and s under some conditions and orders γ,ρ∈(0,1] such that γ≤ρ. In addition, we obtain some inclusion relations between these concepts.

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Author Biographies

Ömer Kişi , Bartın University

Department of Mathematics, Faculty of Sciences, Turkey

Erhan Güler , Bartın University

Department of Mathematics, Faculty of Sciences, Turkey

References

L. A. Zadeh, Fuzzy sets, Inf. Control, 8(3), 338–353, 1965.

A. Kaufmann, Introduction to the theory of fuzzy subsets, New York: Academic Press, 1975.

B. Liu and Y. K. Liu, Expected value of fuzzy variable and fuzzy expected value models, IEEE Trans. Fuzzy Syst., 10(4), 445–450. 2002.

B. Liu, Theory and practice of uncertain programming, Physica-Verlag, Heidelberg, 2002.

B. Liu, Inequalities and convergence concepts of fuzzy and rough variables, Fuzzy Optim. Decis. Mak., 2(2), 87–100, 2003.

B. Liu, A survey of credibility theory, Fuzzy Optim. Decis. Mak., 5(4), 387–408, 2006.

B. Liu, Uncertainty theory, 2nd ed., Springer-Verlag, Berlin, 2007.

E. Savaş, Ö. Kişi and M. Gürdal, On statistical convergence in credibility space, Numer. Funct. Anal. Optim., 43(8) (2022), 987-1008.

Ö. Kişi, M. Gürdal and E. Savaş, On lacunary convergence in credibility space, Facta Univ. Ser. Math. Inform., 37(4) (2022), 683-708.

H. Fast, Sur la convergence statistique, Colloquium Mathematicae 2 1951, 241-244.

A.D. Gadjiev and C. Orhan, Some approximation theorems via statistical convergence, The Rocky Mountain Journal of Mathematics 32 (2002), 129–138.

R. Çolak, Statistical convergence of order α, Modern Methods in Analysis and Its Applications, New Delhi, Anamaya Publishers (2010), 121–129.

J.A. Fridy and C. Orhan, Lacunary statistical convergence, Pacific J. Math. 160 (1993), 43-51.

M. Et and H. Şengül, Some Cesaro-Type summability spaces of order α and lacunary statistical convergence of order α, Filomat 28 (2014), 1593-1602.

H. Şengül and M. Et, f-Lacunary statistical convergence and strong f-lacunary summability of order α, Filomat 32 (2018), 4513-4521.

H. Nakano, Concave modulars, Journal of the Mathematical Society of Japan 5 (1953), 29-49

R. Çolak, Lacunary strong convergence of difference sequences with respect to a modulus function, Filomat 17 (2003), 9-14.

J. Connor, On strong matrix summability with respect to a modulus and statistical convergence, Canad. Math. Bull., 32 (1989), 194-198.

M. Et, Strongly almost summable difference sequences of order m defined by a modulus, Stud. Sci. Math. Hung. 40 (2003), 463-476.

I.S. Ibrahim, R. Çolak, On strong lacunary summability of order α with respect to modulus functions, Ann. Univ. Craiova Math. Comput. Sci. Ser., 48(1) (2021), 127-136.

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Published

2023-02-02

How to Cite

Kişi , Ömer, & Güler , E. (2023). A Study on Lacunary Summability of Order α with respect to Modulus Function for Fuzzy Variables in Credibility Spaces. International Conference on Innovative Academic Studies, 2, 14–18. Retrieved from https://as-proceeding.com/index.php/icias/article/view/9

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Conference Papers