$\rho-$Statistical Convergence of Order $\alpha$ in Partial Metric Spaces

Abstract

In the present study, we introduce and study the notions of $\rho-$statistically convergence and $\rho-$statistically boundedness of order $\alpha$ in a partial metric space $(X,p)$ and a relation between these two concepts is established, where $\rho=(\rho_n)$ is a non decreasing sequence of positive real numbers. Apart from this, we explored the inclusion relations between $\rho-$statistical convergence and $\rho-$statistical boundedness with the variation of the sequence $\rho=(\rho_n)$.