Statistically unbounded p-convergence in lattice-normed Riesz spaces

TL;DR

This paper introduces and studies statistically unbounded p-convergence in lattice-normed Riesz spaces, exploring its properties and relationships with other statistical convergence types.

Contribution

It defines the concept of statistically unbounded p-convergence and analyzes its connections to existing statistical convergence notions in Riesz spaces.

Findings

Established properties of statistically unbounded p-convergence.

Derived relations between this convergence and other statistical convergences.

Provided theoretical framework for future research in lattice-normed Riesz spaces.

Abstract

The statistically unbounded $p$-convergence is an abstraction of the statistical order, unbounded order, and $p$-convergences. We investigate the concept of the statistically unbounded convergence on lattice-normed Riesz spaces with respect to statistical p-decreasing sequences. Also, we get some relations between this concept and the other kinds of statistical convergences on Riesz spaces.