DEFERRED CESARO STATISTICAL CONVERGENCE OF MARTINGALE SEQUENCE AND KOROVKIN-TYPE APPROXIMATION THEOREMS

摘要

In the present paper, we introduce and study the concepts of statistical convergence and statistical summability for martingale sequences of random variables via deferred Ces??ro mean. We then establish an inclusion theorem concerning the relation between these two beauti-ful and potentially useful concepts. Also, based upon our proposed notions, we state and prove new Korovkin-type approximation theorems with algebraic test functions for a martingale se-quence over a Banach space. Moreover, we demonstrate that our theorems effectively extend and improve most (if not all) of the previously existing results (in statistical and classical versions). Finally, by using the generalized Bernstein polynomials, we present an illustrative example of a martingale sequence in order to demonstrate that our established theorems are stronger than their traditional and statistical versions.