*(English)*Zbl 06174708

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] $\left\{{A}_{k}\right\}$ is a Wijsman statistically convergent sequence,

[ii] $\left\{{A}_{k}\right\}$ is a Wijsman statistically Cauchy sequence,

[iii] $\left\{{A}_{k}\right\}$ is a sequence for which there is a Wijsman convergent sequence $\left\{{B}_{k}\right\}$ such that ${A}_{k}={B}_{k}$ almost all $k$. 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.

##### MSC:

40A05 | Convergence and divergence of series and sequences |

46E25 | Rings and algebras of continuous, differentiable or analytic functions |