On Deferred Statistical Convergence of Sequences of Sets in Metric Space
On Deferred Statistical Convergence of Sequences of Sets in Metric Space
In this paper mainly, Wijsman deferred statistical convergence of sequence of sets in an arbitrary metric space is defined and some basic theorems are given. Besides new results, some results in this paper are the generalization of the results given in [3], [15] and [18].
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- Agnew R. P., On Deferred Ces`aro Mean, Comm. Ann. of Math. 33, 413-421 (1932).
- Aubin J. P., Frankowska H., Set-Valued Analysis, Birkhauser, Basel , 133-155 (1986).
- Beer G., On the compactness theorem for sequences of closed sets, Math. Balkanica 16, 327-338 (2002).
- Buck R. C., The measure theoretic approch to density, Amer. J. Math., 68, 560-580 (1946).
- Fast H., Sur la convergece statistique, Colloq. Math. 2, 241-244 (1951).
- Fridy J.A., On statistical convergence, Analysis 5, 301-313 (1985).
- Fridy J.A., Miller H. I., A matrix characterization of statistical convergence, Analysis 11, 59-66 (1991).
- Fridy. J.A., Orhan C., Lacunary statistical summability, J. Math. Anal. Appl. 173(2), 497-504 (1993).
- Kaya E., Küçükaslan M. and Wagner R., On Statistical Convergence and Statistical Monotonicity, Annales Univ. Sci. Budapest. Sect. Comp. 39, 257-270 (2013).
- Kolk K., Matrix summabilitiy of statistically sequences, Analysis 13, 77-83 (1993).
- Kuratowski C., Topology, Academic Press, New York vol 1, (1966).
- Küçükaslan M., Yılmaztürk M., Deferred statistical convergence, Kyunpook Mathematical Journal (under review) (2013).
- Maddox I.J., Elements of Functional Analysis, Cambridge University Press, (1970).
- Mursaleen M., λ-statistical convergence, Math. Slovaca 50, 111-115 (2000).
- Nuray F., Rhoades B. E., Statistical convergence of sequences of sets Fasciculi Mathematici E-Notes 49, 87-99 (2012).
- Peterson Gordon M., Regular matrix transformation, McGraw-hill. Pub. Company limited London (1966).
- Steinhaus H., Sur la convergence ordinaire et la convergence asymtotique, Colloq.Math. 2, 73-74 (1951).
- Ulusu U., Nuray F., Lacunary statistical convergence of sequence of sets, Progress in Applied Mathematics 4(2), 99-109 (2012).
- Wijsman R.A., Convergence of sequences of convex sets, cones and functions, Bulletin of the American Mathematical Socaity 70, 186-188 (1964).