On Statistical Convergence Of Order ${\alpha}$ In Partial Metric Spaces

TL;DR

This paper introduces and analyzes new concepts of statistical convergence and summability of order alpha in partial metric spaces, exploring their inclusion relations and introducing lambda-statistical convergence.

Contribution

It presents novel definitions of statistical convergence and summability of order alpha in partial metric spaces, along with their inclusion relations and the concept of lambda-statistical convergence.

Findings

Defined statistical convergence of order alpha in partial metric spaces

Established inclusion relations between different convergence concepts

Introduced lambda-statistical convergence and related sequence spaces

Abstract

The present study introduces the notions of statistical convergence of order $\alpha$ and strong $p-$ Ces\`{a}ro summability of order $\alpha$ in partial metric spaces. Also, we examine the inclusion relations between these concepts. In addition, we introduce the notion of $\lambda -$% statistical convergence of order $\alpha$ in partial metric spaces while providing relations linked to these sequence spaces.