Yıl 2018, Cilt 47, Sayı 4, Sayfalar 889 - 896 2018-08-01
| | | |

## Statistical convergence of sequences of sets in hyperspaces

#### Sevda Sağıroğlu [1] , Mehmet Ünver [2]

##### 34 63

The concept of statistical convergence in an arbitrary topological space is nothing new, it is actually a self-evident concept that comes through the structure of that space. In this paper, by considering the well known topologies on hyperspaces, we investigate the characterizations of statistical convergence of sequences of sets in the realm of these structures.
Hyperspaces, weak topologies, statistical convergence
• Attouch, H., Lucchetti, R. and Wets, R. The topology of the $\rho$-Hausdorff distance, Ann. Mat. Pura. Appl. 160, 303320, 1991.
• Beer, G. Metric spaces with nice closed balls and distance function for closed sets, Bull. Austral. Math. Soc. 35, 8196, 1978.
• Beer, G. On Mosco convergence of convex sets, Bull. Austral. Math. Soc. 95, 737739, 1988.
• Beer, G. An embedding theorem for the Fell topology, Michigan Math. J. 35, 39, 1988.
• Beer, G. Topologies on closed and convex sets, Math. App. 268, Kluwer Academic Publishers Group, Dordrecht, 1993.
• Cakalli, H. and Khan, M. K. Summability in topological spaces, Appl. Math. Lett. 24 (3), 348352, 2011.
• Cakalli, H. Lacunary statistical convergence in topological groups, Indian J. Pure Appl. Math. 26 (2), 113119, 1995.
• Connor, J. S. The statistical and strong p-Cesàro convergence of sequences, Analysis 8, 4763, 1988.
• Fast, H. Sur la convergence statistique, Colloq. Math. 2, 241244, 1951.
• Freedman, A.R. and Sember, J.J. Densities and summability, Pacic J. Math. 95, 293305, 1981.
• Fridy, J.A. On statistical convergence, Analysis 5, 301313, 1985.
• Fridy, J.A. and Miller H. I. A matrix characterization of statistical convergence, Analysis 11, 5966, 1991.
• Fridy, J.A. and Orhan, C. Statistical limit superior and limit inferior, Proc. Amer. Math. Soc. 125 (12), 36253631, 1997.
• Khan, M.K. and Orhan, C. Matrix characterization of A-statistical convergence, J. Math. Anal. Appl. 335, 406417, 2007.
• Kişi, Ö. and Nuray, F. New convergence definitions for sequences of sets, Abst. Appl. Anal. Volume 2013, Article ID 852796.
• Kolk, E. Matrix summability of statistically convergent sequences, Analysis 13 (1-2), 7783, 1993.
• Kostyrko, P., Macaj, M. and alát, T. I-convergence, Real Anal. Exchange 26 (2), 669686, 2000.
• Maddox, I.J. Statistical convergence in a locally convex space, Math. Proc. Cambridge Philos. Soc. 104 (1), 141145, 1988.
• Maio, G. D. and Ko£inac, L.D.R. Statistical convergence in topology, Topology Appl. 156, 2845, 2008.
• Miller, H.I. A measure theoretical subsequence characterization of statistical convergence. Trans. Amer. Math. Soc. 347 (5), 18111819, 1995.
• Mosco, U. Convergence of convex sets and of solutions of variational inequalities, Advances in Math. 3 (4), 510585, 1969.
• Nuray, F. and Rhoades, B.E. Statistical convergence of sequences of sets, Fasc. Math. 49, 8799, 2012.
• Pancaroğlu, N. and Nuray, F. Invariant statistical convergence of sequences of sets with respect to a modulus function, Abst. Appl. Anal. Volume 2014, Article ID 818020.
• Salát, T. On statistically convergent sequences of real numbers, Math. Slovaca, 30 (2), 139150, 1980.
• Savaş, E. On I-lacunary statistical convergence of order $\alpha$ for sequences of sets, Filomat, 29 (6), 2015.
• Unver, M., Khan, M. K. and Orhan, C. A-distributional summability in topological spaces, Positivity, 18 (1), 131145, 2014.
• Wets, R. Convergence of convex functions, variational inequalities, and convex optimization problems, Variational inequalities and complementarity problems 375403, 1980.
• Wijsman, R.A. Convergence of sequences of convex sets, cones and functions, II. Trans. Amer. Math. Soc. 123, 3245, 1966.
Birincil Dil en Matematik Matematik Yazar: Sevda Sağıroğlu (Sorumlu Yazar) Yazar: Mehmet Ünver
 Bibtex @araştırma makalesi { hujms453118, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {Hacettepe Üniversitesi}, year = {2018}, volume = {47}, pages = {889 - 896}, doi = {}, title = {Statistical convergence of sequences of sets in hyperspaces}, key = {cite}, author = {Sağıroğlu, Sevda and Ünver, Mehmet} } APA Sağıroğlu, S , Ünver, M . (2018). Statistical convergence of sequences of sets in hyperspaces. Hacettepe Journal of Mathematics and Statistics, 47 (4), 889-896. Retrieved from http://dergipark.gov.tr/hujms/issue/38872/453118 MLA Sağıroğlu, S , Ünver, M . "Statistical convergence of sequences of sets in hyperspaces". Hacettepe Journal of Mathematics and Statistics 47 (2018): 889-896 Chicago Sağıroğlu, S , Ünver, M . "Statistical convergence of sequences of sets in hyperspaces". Hacettepe Journal of Mathematics and Statistics 47 (2018): 889-896 RIS TY - JOUR T1 - Statistical convergence of sequences of sets in hyperspaces AU - Sevda Sağıroğlu , Mehmet Ünver Y1 - 2018 PY - 2018 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 889 EP - 896 VL - 47 IS - 4 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2016 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Statistical convergence of sequences of sets in hyperspaces %A Sevda Sağıroğlu , Mehmet Ünver %T Statistical convergence of sequences of sets in hyperspaces %D 2018 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 47 %N 4 %R %U ISNAD Sağıroğlu, Sevda , Ünver, Mehmet . "Statistical convergence of sequences of sets in hyperspaces". Hacettepe Journal of Mathematics and Statistics 47 / 4 (Ağustos 2018): 889-896.