On statistical convergence of sequences of closed sets in metric spaces
-
Dimitrios Georgiou
,
Athanasios Megaritis
Abstract
In this paper, we do further investigations on the statistical inner and outer limits of sequences of closed sets in metric spaces, which were introduced by Nuray, Rhoades, and Talo, Sever, Başar, and generalize the conventional Painleve-Kuratowski inner and outer limits. Also, we provide criteria for checking statistical Wijsman and Hausdorff set convergences and we examine the relationship between Kuratowski and Wijsman statistical convergence. A closer look on the concept of statistical Cauchyness, with respect to the Hausdorff “extended” metric h, completes this research.
The third author G. A. Prinos would like to thank the General Secretariat for Research and Technology (GSRT) and the Hellenic Foundation for Research and Innovation (HFRT) for the financial support of this research (Scholarship Code: 1582).
The fourth author F. Sereti would like to thank the General Secretariat for Research and Technology (GSRT) and the Hellenic Foundation for Research and Innovation (HFRT) for the financial support of this research (Scholarship Code: 2547).
Acknowledgement
The authors would like to thank the referee for the careful reading of the paper and the useful comments.
(Communicated by Gregor Dolinar )
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© 2021 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- Regular papers
- Prof. RNDr. Michal Fečkan, DrSc. – Sexagenarian?
- Tribonacci numbers with two blocks of repdigits
- Padovan numbers that are concatenations of two distinct repdigits
- On the 2-rank and 4-rank of the class group of some real pure quartic number fields
- A general inverse matrix series relation and associated polynomials – II
- Some hardy type inequalities with finsler norms
- Starlikeness and convexity of the product of certain multivalent functions with higher-order derivatives
- Block Hessenberg matrices and spectral transformations for matrix orthogonal polynomials on the unit circle
- How is the period of a simple pendulum growing with increasing amplitude?
- Fourier transforms of convolution operators on orlicz spaces
- Some characterizations of property of trans-Sasakian 3-manifolds
- P-Adic metric preserving functions and their analogues
- On statistical convergence of sequences of closed sets in metric spaces
- A characterization of the uniform convergence points set of some convergent sequence of functions
- A nonparametric estimation of the conditional ageing intensity function in censored data: A local linear approach
- Donsker’s fuzzy invariance principle under the Lindeberg condition
- Characterization of generalized Gamma-Lindley distribution using truncated moments of order statistics
- Matrix variate pareto distributions
- Global exponential periodicity and stability of neural network models with generalized piecewise constant delay
- Optimal inequalities for contact CR-submanifolds in almost contact metric manifolds
