ON RHO-STATISTICAL CONVERGENCE IN TOPOLOGICAL GROUPS

Year 2022, Volume: 4 Issue: 1, 9 - 14, 30.04.2022

Hacer Şengül Kandemir

https://doi.org/10.47087/mjm.1092559

Cited By: 4

Abstract

In this study, by using definition of rho-statistical convergence which
was defined by Cakalli [5], we give some inclusion relations between the sets
of rho-statistical convergence and statistical convergence in topological groups.

Keywords

Topological groups , statistical convergence , rho-statistical convergence

References

• N. D. Aral, and M. Et, Generalized difference sequence spaces of fractional order defined by Orlicz functions, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 69 (1) (2020) 941-951.
• N. D. Aral, and H. Sengul Kandemir, I-Lacunary Statistical Convergence of order of Difference Sequences of Fractional Order, Facta Universitatis(NIS) Ser. Math. Inform. 36 (1) (2021) 43-55.
• N. D. Aral, and S. Gunal, On M_lambda_m;n-statistical convergence, Journal of Mathematics (2020), Article ID 9716593, 8 pp.
• A. Caserta, Di M. Giuseppe, and L. D. R. Kocinac, Statistical convergence in function spaces, Abstr. Appl. Anal. (2011), Art. ID 420419, 11 pp.
• H. Cakalli, A variation on statistical ward continuity, Bull. Malays. Math. Sci. Soc. 40 (2017) 1701-1710.
• H. Cakalli, Lacunary statistical convergence in topological groups, Indian J. Pure Appl. Math. 26(2) (1995) 113-119.
• H. Cakalli, A study on statistical convergence, Funct. Anal. Approx. Comput. 1(2) (2009) 19-24.
• M. Cinar, M. Karakas, and M. Et, On pointwise and uniform statistical convergence of order alpha for sequences of functions, Fixed Point Theory Appl. 2013(33) (2013) 11 pp.
• R. Colak, Statistical convergence of order alpha; Modern Methods in Analysis and Its Applications, New Delhi, India: Anamaya Pub, 2010 (2010) 121-129.
• J. S. Connor, The Statistical and strong p-Cesaro convergence of sequences, Analysis 8 (1988) 47-63.
• M. Et, R. Colak, and Y. Altin, Strongly almost summable sequences of order alpha; Kuwait J. Sci. 41(2) (2014) 35-47.
• M. Et, S. A. Mohiuddine, and A. Alotaibi, On lambda-statistical convergence and strongly lambda-summable functions of order alpha, J. Inequal. Appl. 2013(469) 2013 8 pp.
• M. Et, H. Altinok, and R. Colak, On lambda-statistical convergence of difference sequences of fuzzy numbers, Information Sciences, 176(15) (2006) 2268-2278.
• H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951) 241-244.
• J. Fridy, On statistical convergence, Analysis 5 (1985) 301-313.
• A. D. Gadjiev, and C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. Math. 32(1) (2002) 129-138.
• M. Isik, and K. E. Akbas, On lambda-statistical convergence of order alpha in probability, J. Inequal. Spec. Funct. 8(4) (2017) 57-64.
• M. Isik, and K. E. Akbas, On asymptotically lacunary statistical equivalent sequences of order alpha in probability, ITM Web of Conferences 13 (2017) 01024.
• E. Kolk, The statistical convergence in Banach spaces, Acta Comment. Univ. Tartu 928 (1991) 41-52.
• M. Mursaleen, lambda-statistical convergence, Math. Slovaca, 50(1) (2000) 111-115.
• T. Salat, On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980) 139-150.
• H. Sengul, and M. Et, On I-lacunary statistical convergence of order alpha of sequences of sets, Filomat 31(8) (2017) 2403-2412.
• H. Sengul, On Wijsman I-lacunary statistical equivalence of order (eta; mu), J. Inequal. Spec. Funct. 9(2) (2018) 92-101.
• H. Sengul, and M. Et, f-lacunary statistical convergence and strong f-lacunary summa-bility of order alpha, Filomat 32(13) (2018) 4513-4521.
• H. Sengul, and M. Et, On (lambda; I)-statistical convergence of order alpha of sequences of function, Proc. Nat. Acad. Sci. India Sect. A 88(2) (2018) 181-186.
• M. Et, M. Cınar, and H. Sengul, On Delta^m-asymptotically deferred statistical equivalent sequences of order alpha, Filomat 33(7) (2019) 1999-2007.
• H. Sengul, and O. Koyun, On (lambda;A)-statistical convergence of order alpha, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat. 68(2) (2019) 2094-2103.
• 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.