Deferred statistical order convergence in Riesz spaces

TL;DR

This paper introduces and explores the concept of deferred statistical convergence within Riesz spaces, establishing its relation to other statistical convergence types and expanding the theoretical framework of convergence in ordered vector spaces.

Contribution

The paper defines deferred statistical convergence in Riesz spaces and analyzes its relationship with existing statistical convergence concepts, advancing the theoretical understanding.

Findings

Deferred statistical convergence is formally defined in Riesz spaces.

Relations between deferred statistical convergence and other statistical convergences are established.

Theoretical properties of deferred statistical convergence are analyzed.

Abstract

Some types of statistical convergence such as statistical order and deferred statistical convergences have been studied and investigated in Riesz spaces, recently. In this paper, we introduce the concept of deferred statistical convergence in Riesz spaces with order convergence. Moreover, we give some relations between deferred statistical order convergence and other kinds of statistical convergences.