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 [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-Cesaro convergence of order alpha. Furthermore, some examples are displayed here to show that these concepts are not same with the concepts defined in [7].