Matrix summability of sequences of sets

Document Type : Original Article

Author

Fatih Nuray

Department of Mathematics, Afyon Kocatepe University, Afyonkarahisar, Turkey

10.22034/kjm.2022.327963.2476

Abstract

In this paper the definition of strong Cesaro summability of sequences of closed sets with respect to a modulus is extended to a definition of strong $T$-summability with respect to a modulus when $T$ is a nonnegative regular matrix summability method. Also, we show that if a sequence of closed sets is strongly $T$-summable with respect to an arbitrary modulus,  then it is $T$-statistically convergent and that $T$-statistical convergence and strong $T$-summability with respect to a modulus are equivalent on the bounded sequences of closed sets.

Keywords

Sequence of sets

Wijsman convergence

Matrix transformation

Regular matrix

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