Lacunary statistical and lacunary strongly convergence of generalized difference sequences of fuzzy numbers

Abstract

The purpose of this paper is to introduce the concepts of lacunary statistical convergence and lacunary strongly convergence of generalized difference sequences of fuzzy numbers. We give some relations related to these concepts. We show that lacunary Delta(m)-statistical convergence and lacunary strongly Delta(m)((p))-convergence are equivalent for Delta(m)-bounded sequences of fuzzy numbers. We also introduce the concept of lacunary Delta(m)-statistically Cauchy sequence and show that it is equivalent to the lacunary Delta(m)-statistical convergence. (c) 2006 Elsevier Ltd. All rights reserved.