ρ ˜ Katlı Bessel I_2-Δ_θ^n-Asimptotik İstatistiksel Denk Çift Dizilerin Bazı Özellikleri

Abstract

Dizi uzayları ve toplanabilirlik teorisi çerçevesinde, klasik yakınsama ve sınırlılık kavramlarının teorik temelleri üzerine önemli ilerlemeler kaydedilmiş olmakla birlikte, yenilikçi yakınsama yöntemlerinin araştırılması hala kritik bir alan olarak öne çıkmaktadır. Literatürde, özellikle Bessel fonksiyonlarının bu teorik yapılarla entegrasyonu yönünde belirgin bir eksiklik bulunmaktadır. Bu çalışma, çift diziler için ρ̃ katlı Bessel I_2-Δ_θ^n-asimptotik istatistiksel denklik ve güçlü Bessel I_2-Δ_θ^n-asimptotik denklik kavramlarını tanıtarak, bu boşluğu doldurmayı ve söz konusu kavramlar arasındaki kapsama ilişkilerini kapsamlı bir biçimde incelemeyi amaçlamaktadır. Bessel fonksiyonlarının bu bağlamda teorilere dahil edilmesi, yalnızca matematiksel analiz alanındaki mevcut teorik çerçeveleri genişletmekle kalmayıp, aynı zamanda alanın ileri düzeydeki araştırmalarına ve uygulamalı problemlerin çözümüne yönelik sağlam bir temel teşkil etmektedir. Bu yenilikçi kavramlar, Bessel fonksiyonlarıyla ilişkili dizi davranışlarının daha derin bir şekilde anlaşılmasına katkıda bulunmakta ve bu anlayışın matematiksel uygulamalarda kullanılabilirliğini artırmaktadır.

Keywords

• Asimptotik denklik
• Bessel istatistiksel yakınsaklık
• Lacunary dizi

Some Properties of Bessel I_2-Δ_θ^n-Asymptotically Statistical Equivalent Double Sequence of Order ρ ˜

Abstract

In the context of sequence spaces and summability theory, significant progress has been made in the theoretical foundations of classical concepts such as convergence and boundedness. However, the exploration of innovative convergence methods continues to emerge as a critical area of research. A notable gap in the literature is the integration of Bessel functions into these theoretical frameworks. This study aims to fill this gap by introducing the concepts of Bessel I_2-Δ_θ^n-asymptotically statistical equivalence of order ρ ˜ and strong Bessel I_2-Δ_θ^n-asymptotically equivalence of order ρ̃ for double sequences, examining the comprehensive interrelations of these concepts. The inclusion of Bessel functions in these theories not only extends the existing theoretical frameworks within mathematical analysis but also provides a solid foundation for further research and the solution of applied problems in the field. These innovative concepts contribute to a deeper understanding of sequence behavior related to Bessel functions and enhance their applicability in mathematical applications.

Keywords

• Asymptotical equivalence
• Bessel statistical convergence
• Lacunary sequence

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