In this paper, the authors generalized statistical convergence using Kuratowski convergence, which was introduced in [K. Kuratowski, Topology. Vol. I. New edition, revised and augmented. New York-London: Academic Press; Warszawa: PWN-Polish Scientific Publishers. (1966; Zbl 0158.40802)], Wijsman convergence, which was introduced in [R. A. Wijsman, Bull. Am. Math. Soc. 70, 186–188 (1964; Zbl 0121.39001), Trans. Am. Math. Soc. 123, 32–45 (1966; Zbl 0146.18204)] and Hausdorf convergence, which was introduced in [F. Hausdorff, Grundzüge der Mengenlehre. Mit 53 Figuren im Text. Leipzig: Veit Comp. (1914; Zbl 45.0123.01)]. They give the definitons of Kuratowski, Wijsman and Hausdorff statistical convergence of sequences of sets. Then they proved the theorem that says, description
[i] is a Wijsman statistically convergent sequence,
[ii] is a Wijsman statistically Cauchy sequence,
[iii] is a sequence for which there is a Wijsman convergent sequence such that almost all . are equivalent.
Moreover, they give some Tauberian conditions for Wijsman and Hausdorf statistical convergences.
Finally, they introduced Cesàro summable, strongly Cesàro summable, strongly p-Cesàro summable, almost converget, strongly almost convergent and strongly p-almost convergent for above definitions, and then they give some basic theorems of those new notions.