ON GENERALIZED STATISTICAL CONVERGENCE OF ORDER alpha OF FUNCTIONS

In this paper, we introduce the concept of generalized statistical convergence of measurable functions of order $\alpha $ for $0<\alpha \leq 1$ at $\infty $ and at a point $c\in \mathbb{R}$. In addition to this, we defined generalized strongly $p$-Ces\`{a}ro summability ($0<p<\infty $) of a locally integrable function at $\infty $ and at a point $c\in \mathbb{R}$. Using these definitions we present some basic results.