Restricted Uniform Density and Corresponding Convergence Methods

S. A. Mohiuddine, C. Belen

Recently, the idea of asymptotic density of order $\alpha$ has been introduced by Bhunia et. al. in [7]. In the present paper we introduce the notion of uniform density of order $\alpha$ and define and study related convergence methods so-called $I_u$-convergence of order $\alpha$ and uniform strong $p$-Cesàro convergence of order $\alpha$. Furthermore, some examples are displayed here to show that these concepts are not same with the concepts defined in [7].