arXiv subjects
Publications and source records attributed to Mahendranath Paul.
In this paper we study $I^K$-convergence of functions with respect to probabilistic norm $ν$ which is a generalization of $I^*_ν$-convergence in probabilistic norm spaces. We also study on $I^K$-Cauchy functions and $I^K$-limit points with respect to probabilistic norm $ν$ in the same space.
In this paper, we study on weak $I^K$-Cauchy condition as a generalization of weak $I^*$-Cauchy condition in a normed space. We investigate the relationship between weak $I$-Cauchy and weak $I^K$-Cauchy sequences using $AP(I,K)$-condition. Also we study on weak* $I^K$-Cauchy condition and weak $I^K$-divergence of sequences in the same space.
The main object of this paper is to study the concept of weak $I^K$-convergence, a generalization of weak $I^*$-convergence of sequences in a normed space, introducing the idea of weak* $I^K$-convergence of sequences of functionals where $I,K$ are two ideals on $\mathbb{N}$, the set of all positive integers. Also we have studied the ideas of weak $I^K$ and weak* $I^K$-limit points to investigate the properties in the same space.
In this paper we study the idea of strong-I^K-convergence of functions which is common generalization of strong-I*-convergence of functions in probabilistic metric spaces. We also study strong-I^K-limit points of functions in the same space.
In this paper we have studied some important topological properties and characterization of I^K-convergence of functions which is a common generalization of I*-convergence of functions. We also introduce the idea of I^K*-convergence and I^K-limit points of functions.