Restricted Uniform Density and Corresponding Convergence Methods

Abstract

Recently, the idea of asymptotic density of order $\alpha$ has been introduced by Bhunia et. al. in [4]. In the present paper we introduce the notion of uniform density of order $\alpha$ and define and study related convergence methods so-called Iu-convergence of order and uniform strong p-Cesaro convergence of order $\alpha$. Furthermore, some examples are displayed here to show that these concepts
are not same with the concepts defined in [4].