This talk is mainly concerned with two generalizations of convergence of sequences called I-convergence and I∗-convergence. We will mention some other generalizations of limit which are related to I-convergence, e.g Banach limit and statistical convergence. 1 Generalizations of limit The notion of limit is one of the central notions in mathematical analysis. No wonder it was generalized by math...

Abstract. The aim of this paper is to study the notion of lacunary I-convergence in probabilistic normed spaces as a variant of the notion of ideal convergence. Also lacunary I-limit points and lacunary I-cluster points have been defined and the relation between them has been established. Furthermore, lacunary Cauchy and lacunary I-Cauchy sequences are introduced and studied. Finally, we provid...

Some results on the sets of almost convergent, statistically uniformly $I$-convergent subsequences $(s_{n})$ have been obtained by many authors via establishing a one-to-one correspondence between interval $(0,1]$ and collection all given sequence $s=(s_{n})$. However, there are still some gaps in existing literature. In this paper we plan to fill with new results. them easily derived from earl...

An ideal I is a family of subsets of positive integers N which is closed under taking finite unions and subsets of its elements. In this paper we have introduced ideal convergent sequences of fuzzy real numbers usingσ-uniform density. Furthermore, inclusion between Iσ-convergence and invariant convergence also Iσ-convergence and [Vσ]Fp -convergence were given.