Some Inclusion Relations Between Lacunary Methods on Probabilistic Normed Spaces

A lacunary sequence is an increasing sequence Ѳ = (kr) of positive integerssuch that k0 = 0 and kr − kr−1 ∞1 as r ∞1. In this paper we introducelacunary statistical convergence on probabilistic normed space (briefly PN spaces)and establish some inclusion relations between the sets of statistically convergentand lacunary statistically convergent sequences on PN spaces. We also definedlacunary statistical Cauchy sequence in these spaces and prove that it is equivalentto lacunary statistical convergent sequence.