Multidimensional Asymptotically Deferred Statistical Equivalent Measurable Functions

Abstract

In 1932 Agnew presented the concept of deferred Cesáro means. Following Agnew's results, Küçükaslan and Yılmaztürk introduced the definition of deferred statistical convergence for sequences. Also, Patterson studied the notion of asymptotically equivalent sequences. In 2020, Savas generalized Patterson's definition for measurable functions by considering the concept of deferred statistical convergence. The goal of this article is to extend Savas results to higher dimension. To accomplish this we introduce the concepts of double asymptotically deferred statistical equivalence and double strongly asymptotically deferred statistical equivalence in the Pringsheim sense by using two nonnegative bivariate measurable real valued functions on (1, ?) × (1, ?). Additionally, we examine some important results. © 2022 American Institute of Physics Inc.. All rights reserved.