Korean J. Math. Vol. 30 No. 4 (2022) pp.679-686
DOI: https://doi.org/10.11568/kjm.2022.30.4.679

The meaning of the concept of lacunary statistical convergence in G-metric spaces

Article Sidebar

PDF
Published: Dec 30, 2022
Keywords:
Selected:Statistical convergence, lacunary sequences, G-metric spaces
Mathematics Subject Classification:
40G15, 40A35

Main Article Content

Şerife Selcan Küçük
Institute of Science, Necmettin Erbakan University, Eregli, Konya 42310, Turkey
Hafize Gümüş
Department of Mathematics and Science Education, Necmettin Erbakan University, Eregli, Konya 42310, Turkey
https://orcid.org/0000-0001-8972-5961

Abstract

In this study, the concept of lacunary statistical convergence is studied in G-metric spaces. The G-metric function is based on the concept of distance between three points. Considering this new concept of distance, we examined the relationships between $GS,$ $GS_{\theta },G\sigma _{1}$ and $GN_{\theta} $ sequence spaces.



Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License.

References

[1] R. Abazari, Statistical convergence in g-metric spaces, Filomat 36 (5) (2022), 1461–1468. Google Scholar

[2] T. V. An, N. V. Dung and V. T. L. Hang, A new approach to fixed point theorems on G-metric spaces, Topol. Appl. 160 (12) (2013), 1486–1493. Google Scholar

[3] J. Connor, The statistical and strong p-Ces ́aro convergence of sequences, Analysis 8 (1988), 47–63. Google Scholar

[4] B. H. Dhage, Generalized metric space and mapping with fixed point, Bull. Cal. Math. Soc. 84 (1992), 329–336. Google Scholar

[5] P. Erdos and G. Tenenbaum, Sur les densities de certaines suites d’entiers, Proc. London. Math. Soc. 3 (59) (1989), 417–438. Google Scholar

[6] H. Fast, Sur la convergence statistique, Colloquium Mathematicum 2 (1951), 241–244. Google Scholar

[7] A. R. Freedman, J. Sember and M. Raphael, Some Cesa`ro-type summability spaces, Proc. London Math. Soc. 37 (3) (1978), 508–520. Google Scholar

[8] J. A. Fridy, On statistical convergence, Analysis 5 (1985), 301–313. Google Scholar

[9] J. A. Fridy and C. Orhan, Lacunary statistical summability, J. Math. Anal. Appl. 173 (1993), 497–504. Google Scholar

[10] Y. U. Gaba, Fixed point theorems in G-metric spaces, J. Math. Anal. Appl. 455 (1) (2017), 528–537. Google Scholar

[11] Y. U. Gaba, Fixed points of rational type contractions in G-metric spaces, Cogent Mathematics, Statistics 5 (1) (2018), 1–14. Google Scholar

[12] S. Gahler, 2-metriche raume und ihre topologische strukture, Math. Nachr. 26(1963), 115–148. Google Scholar

[13] S. Gahler, Zur geometric 2-metriche raume, Reevue Roumaine de Math.Pures et Appl. XI (1966), 664–669. Google Scholar