We give a characterization of lacunary series in the Bloch space of the unit ball in C in terms of Taylor coefficients. We also characterize Bloch functions whose Taylor coefficients are nonnegative. The corresponding problems for BMOA are discussed as well.

In this paper, we study the concepts of lacunary statistical convergent and lacunary statistical Cauchy sequences in probabilistic normed spaces and prove some basic properties.

In this paper, the concept of lacunary almost summability of sequences in locally convex spaces has been defined and investigated. It is also proved Kojima-Schur and SilvarmanToeplitz type theorems for lacunary almost conservatively and lacunary almost regularity of the which transform sequences in a Frechet space into a sequence in an other Frechet space. We also stated that the same results h...

In this article we introduce and study the notions of ∆(r)-lacunary strongly summable, ∆(r)-Cesàro strongly summable, ∆(r)-statistically convergent and ∆(r)-lacunary statistically convergent sequences of fuzzy numbers. Consequently we construct the spaces of these four types of difference sequences and investigate the relationship among these spaces. Further we show that the spaces of ∆(r)-lacu...

Recently in [22], Mursaleen introduced the concept of statistical convergence in random 2-normed spaces. In this paper, we define and study the notion of lacunary ∆-statistical convergence and lacunary ∆-statistical Cauchy sequences in random 2-normed spaces using lacunary density and prove some interesting theorems. Subjclass [2000] : Primary 40A05; Secondary 46A70, 40A99, 46A99.

In this paper‎, ‎following a very recent‎ ‎and new approach‎, ‎we further generalize recently introduced‎ ‎summability methods‎, ‎namely‎, ‎$I$-statistical convergence and‎ ‎$I$-lacunary statistical convergence (which extend the important‎ ‎summability methods‎, ‎statistical convergence and lacunary‎ ‎statistical convergence using ideals of $mathbb{N}$) and‎ ‎introduce the notions of $I$-statis...