A Note on Probability Convergence Defined by Unbounded Modulus Function and $alphabeta$-Statistical Convergence

Abstract

In this paper we define f − αβ-statistical convergence of order γ in probability and f − αβ-strong p-Ces`aro summability of order γ in probability for a sequence of random variables under unbounded modulus function and examine the relation between these two concepts. We show by an example that this notion of f − αβ-statistical convergence of order γ in probability is stronger than αβ-statistical convergence of order γ in probability.