Lacunary statistical convergence defined by an Orlicz function in sequences of fuzzy numbers

Abstract

In the present paper, we introduce the concept of strongly N-theta(beta) (p, F, Delta (m), M)-summable with respect to the Orlicz function M and examine the notions S-theta(beta) (F, Delta (m))-statistical convergence and strong N-theta(beta) (p, F, Delta (m), M)-summability for different two lacunary sequences and beta is an element of(0, 1]. Moreover, we show that a sequence is S-theta(beta) (F, Delta (m))-statistically convergent if it is strongly N-theta(gamma) (p, F, Delta(m), M)-summable, where theta = {k(r)} and theta = {s(r)} are two lacunary sequences and give some inclusion relations between them.