Wijsman asymptotically ideal statistical sequences of order \((\alpha,\beta)\) under decision making

Volume 38, Issue 3, pp 330--340 https://dx.doi.org/10.22436/jmcs.038.03.04

Publication Date: January 07, 2025 Submission Date: August 15, 2024 Revision Date: October 20, 2024 Accteptance Date: November 09, 2024

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Authors

M. M. Mohammed - Department of Mathematics, Applied college at Khulis, University of Jeddah, Yangiobod MFY, G'ijduvon street, House 74, Jeddah, Saudi Arabia. S. K. Sharma - School of Mathematics, Shri Mata Vaishno Devi University, Kakryal, Katra-182320, J\(\&\)K, India. M. Magzoub - Mathematics Department, Applied college-Alkamil, University of Jeddah, Jeddah, Saudi Arabia. R. Kumar - Department of Mathematics, Central University of Jammu, Rahya Suchani (Bagla), Samba-181143, J\(\&\)K, India. A. K. Sharma - Department of Mathematics, Central University of Jammu, Rahya Suchani (Bagla), Samba-181143, J\(\&\)K, India. H. S. Mahgoub - College of Business at Khulis, University of Jeddah, Jeddah, Saudi Arabia. A. A. Gouni - Faculty of Computer Science and Information Technology, Al neelain University, Khartoum, Sudan. A. A. Bakery - Department of Mathematics, Applied college at Khulis, University of Jeddah, Jeddah, Saudi Arabia.

Abstract

The statistical convergence of big data analysis is an essential tool for studying the stability of economic models and many computer vision and machine learning problems. In this paper, we propose the concepts of asymptotically ideal \(\phi\)-statistical equivalent sequences of order \((\alpha,\beta)\) in Wijsman sense by using Musielak-Orlicz function \(\mathcal{M} =(\mathfrak{F}_n)\). We also make an effort to define the concept of asymptotic equivalence, statistical equivalent, \(\phi\)-statistical equivalent sequences of order \((\alpha,\beta)\) in Wijsman sense. We also define the concept of Ces\'{a}ro Musielak-Orlicz asymptoticallly \(\phi\)-equivalent sequences of order \((\alpha,\beta)\) in Wijsman sense and examine some algebraic and topological relationship between these concepts.

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Keywords

• Statistical convergence
• asymptotically equivalence
• Wijsman convergence
• Orlicz function
• Musielak-Orlicz function

MSC

•  40A35
•  40G15
•  40C05

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