A CERTAIN CLASS OF STATISTICAL PROBABILITYCONVERGENCE AND ITS APPLICATIONS TO APPROXIMATION THEOREMS

Applicable Analysis and Discrete Mathematics

article

H. M. Srivastava¹  Bidu Bhusan Jena³  Susanta Kumar Paikray³ 

[1] Department of Mathematics and Statistics University of Victoria Victoria;Department of Medical Research China Medical University Hospital, China Medical University Taichung 40402;Department of Mathematics Veer Surendra Sai University of Technology Burla 768018

关键词: Statistical probability convergence;    Deferred weighted statistical probability convergence;    Sequence of random variables;    Korovkin-type theorems;    Rate of probability convergence.;   

DOI  :  10.2298/AADM190220039S

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

In the present work, we introduce and study the notion of statistical probability convergence for sequences of random variables as well as the concept ofstatistical convergence for sequences of real numbers, which are defined overa Banach space via deferred weighted summability mean. We first establisha theorem presenting a connection between them. Based upon our proposedmethods, we then prove a new Korovkin-type approximation theorem withperiodic test functions for a sequence of random variables on a Banach spaceand demonstrate that our theorem effectively extends and improves most (ifnot all) of the previously existing results (in statistical versions). We alsoestimate the rate of deferred weighted statistical probability convergence andaccordingly establish a new result. Finally, an illustrative example is presented here by means of the generalized Fej´er convolution operators of asequence of random variables in order to demonstrate that our establishedtheorem is stronger than its traditional and statistical versions.

【 授权许可】

Unknown