N. Subramanian’s research while affiliated with SASTRA University and other places

In this paper we study the concept of almost lacunary statistical Cesaro of χ 3 over probabilistic p- metric spaces defined by Musielak Orlicz function. Since the study of convergence in PP-spaces is fundamental to probabilistic functional analysis, we feel that the concept of almost lacunary statistical Cesaro of χ 2 over probabilistic p- metric spaces defined by Musielak in a PP-space would provide a more general framework for the subject.

We study some connections between $\mu$-lacunary strong $\chi ^{3}_{A_{uvw}}$-convergence with respect to a mnk sequence of moduli Musielak–Orlicz function and $\mu$-lacunary $\chi ^{3}_{A_{uvw}}$-statistical convergence, where A is a sequence of four-dimensional matrices $A\left(uvw\right)=\left(a_{k_{1}\cdots k_{r}\ell _{1}\cdots \ell _{s}}^{m_{1}\cdots m_{r}n_{1}\cdots n_{s}}\left(uvw\right)\right)$ of complex numbers.

In this paper we introduce the χ3 fuzzy numbers defined by an Orlicz function and study some of their properties and inclusion results.