Some new lacunary statistical convergence with ideals

Abstract

Abstract In this paper, the idea of lacunary I λ $I_{\lambda}$ -statistical convergent sequence spaces is discussed which is defined by a Musielak-Orlicz function. We study relations between lacunary I λ $I_{\lambda}$ -statistical convergence with lacunary I λ $I_{\lambda}$ -summable sequences. Moreover, we study the I λ $I_{\lambda}$ -lacunary statistical convergence in probabilistic normed space and discuss some topological properties.

Keywords

• Musielak-Orlicz function
• ideal convergence
• lacunary sequences
• probabilistic normed space