Asymptotically deferred statistical equivalent functions of order $ \alpha $ in amenable semigroups

Mikail Et; Hemen Dutta; Naim L. Braha

doi:10.3934/mfc.2023018

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2024, Volume 7, Issue 3: 405-418. Doi: 10.3934/mfc.2023018

This issue Previous Article On the density of translation networks defined on the unit ball Next Article

Asymptotically deferred statistical equivalent functions of order $ \alpha $ in amenable semigroups

1.
Department of Mathematics, Firat University, 23119 Elazığ, Turkey
2.
Department of Mathematics, Gauhati University, Guwahati 781014, India
3.
Department of Mathematics and Computer Sciences University of Prishtina, Avenue Mother Teresa, No-5, 10000 Pristina
4.
Kosova and ILIRIAS Research Institute(http://ilirias.com) Janina, No-2, Ferizaj 70000, Kosova

^* Corresponding author: Naim L. Braha
^* Corresponding author: Naim L. Braha

Received: August 2022

Early access: March 2023

Published: August 2024

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Abstract

The aim of this paper is to study the asymptotic convergence of the sequences. Concretely, we will give the asymptotically statistical convergence of sequences. The asymptotically statistical convergence is studied in many papers including papers [3], [5], [23], [26], [29], [39], [41]. In this paper, we introduce and investigate the concepts of asymptotically deferred statistical equivalent functions of order $ \alpha $ and strong asymptotically deferred statistical equivalent functions of order $ \alpha $ defined on discrete countable amenable semigroups, which generalizes some of the results known in the literature. This is achieved by introducing the Folner sequences and sequences of non-negative integers. Based on this concept we apply it to the approximation theory, and we have proved the Korovkin type theorem and study the rate of convergence for positive linear operators which are deferred statistically convergent of order $ \alpha $.

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Mathematics Subject Classification: Primary: 40A05, 40C05, 46A45.

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