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Rough statistical convergence of sequences in a partial metric space

Sukila khatun, Amar Kumar Banerjee

Abstract

In this paper, using the concept of natural density, we have introduced the notion of rough statistical convergence which is an extension of the notion of rough convergence in a partial metric space. We have defined the set of rough statistical limit points of a sequence in a partial metric space and proved that this set is closed and bounded. Finally, we have found out the relationship between the set of statistical cluster points and the set of rough statistical limit points of sequences in a partial metric space.

Rough statistical convergence of sequences in a partial metric space

Abstract

In this paper, using the concept of natural density, we have introduced the notion of rough statistical convergence which is an extension of the notion of rough convergence in a partial metric space. We have defined the set of rough statistical limit points of a sequence in a partial metric space and proved that this set is closed and bounded. Finally, we have found out the relationship between the set of statistical cluster points and the set of rough statistical limit points of sequences in a partial metric space.
Paper Structure (2 sections, 10 theorems, 8 equations)

This paper contains 2 sections, 10 theorems, 8 equations.

Table of Contents

  1. Introduction and Preliminaries
  2. Rough statistical convergence in partial metric spaces

Key Result

Theorem 2.1

Every rough convergent sequence in a partial metric space $(X,p)$ is rough statistically convergent in $(X,p)$.

Theorems & Definitions (33)

  • Definition 1.1
  • Definition 1.2
  • Definition 1.3
  • Definition 1.4
  • Definition 1.5
  • Definition 1.6
  • Definition 2.1
  • Theorem 2.1
  • proof
  • Remark 2.1
  • ...and 23 more