Matrix summability of sequences of sets

Document Type : Original Article


Department of Mathematics, Afyon Kocatepe University, Afyonkarahisar, Turkey



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.