Results on quasi-statistical limit and quasi-statistical cluster points

Year 2020, Volume: 69 Issue: 1, 646 - 653, 30.06.2020

İlknur Özgüç

https://doi.org/10.31801/cfsuasmas.567734

Cited By: 1

Abstract

In this paper we introduce the concepts of quasi-statistical limit point and quasi-statistical cluster point of a sequence. We give some inclusion results concerning these concepts. We also give the relationship between the Knopp core and quasi-statistical core of a sequence. Finally we state some theorems which deal with quasi-summability and quasi-statistical convergence of a sequence under some assumptions.

Keywords

statistical convergence, quasi-statistical convergence, quasi-statistical limit points, quasi-statistical cluster points

References

• Fast, H., Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244.
• Fridy, J. A., On statistical convergence, Analysis, 5 (1985) 301-313.
• Fridy, J. A., Statistical limit points, Proc. Amer. Math. Soc., 118 (1993), 1187-1192.
• Fridy, J. A. and Orhan,C., Statistical limit superior and limit inferior, Proc. Amer. Math. Soc., 125 (1997), 3625-3631.
• Fridy, J. A. and Orhan, C., Statistical core theorems, J. Math. Anal. Appl., 208 (1997), 520-527.
• Connor, J., The statistical and strong p-Cesàro convergence of sequences, Analysis, 8 (1988) 47-63.
• Connor, J., On strong matrix summability with respect to a modulus and statistical convergence, Canad. Math. Bull., 32 (1989), 194-198.
• Connor, J., Demirci, K. and Orhan, C., Multipliers and factorization for bounded statistically convergence sequences, Analysis (Munich) 22(4) (2002), 321-333.
• Demirci, K. and Orhan, C., Bounded multipliers of bounded A-statistically convergent sequences, Journal of Mathematical Analysis and Applications, 235 (1999), 122-129.
• Ganichev, M. and Kadets, V., Filter convergence in Banach spaces and generalized bases, Taras Banach (Ed.), General Topology in Banach Spaces, NOVA Science Publishers, Huntington, New York (2001), 61-69.
• Sakaoğlu Özgüç, I. and Yurdakadim, T., On quasi-statistical convergence, Commun. Fac. Sci. Univ. Ank. Series A1, 61 (2012), 11-17.
• Šalát, T., On statistically convergent sequences of real numbers, Math. Slovaca, 30(2) (1980), 139-150.
• Schoenberg, I. J., The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361-375.
• Steinhaus, H., Sur la convergence ordinarie et la convergence asymtotique, Colloq. Math., 2 (1951), 73-74.
• Yurdakadim, T., Taş, E. and Sakaoğlu, İ., Approximation of functions by the sequence of integral operators, Appl. Math. Comput., 219 (2012), 3863-3871.
• Zygmund, A., Trigonometric series, 2nd Ed. Cambridge Univ. Press, 1979.