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Journals / Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi / 2020 / Cilt: 20 Sayı: 6

Basic Properties of Statistical Epi-Convergence

İstatistiksel Epi-Yakınsaklık ile İlgili Temel Özellikler

Şükrü Tortop(AFYON KOCATEPE ÜNİVERSİTESİ)0000-0001-5342-7612
Pages
968–974
Publication Date
2020-12-31
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Such situations are studied: Uniform statistical convergence of sequence of functions, statistical epi-limit of compound of sequence of functions, statistical epi-limit of the sum of sequence of functions, the property of epi-limit function if the sequence of functions are lower semi-continuous and the convexity of epi-limit function if each function in the sequence is convex.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we give some basic properties in order to use statistical epi-convergence more efficiently in future studies.
📊
Key Findings & Data:In this paper, we give some basic properties in order to use statistical epi-convergence more efficiently in future studies.
💡
Conclusion & Impact:Such situations are studied: Uniform statistical convergence of sequence of functions, statistical epi-limit of compound of sequence of functions, statistical epi-limit of the sum of sequence of functions, the property of epi-limit function if the sequence of functions are lower semi-continuous and the convexity of epi-limit function if each function in the sequence is convex.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Epi-Yakınsaklık · İstatistiksel Yakınsaklık · Epigraf

Abstract

In this paper, we give some basic properties in order to use statistical epi-convergence more efficiently in future studies. Such situations are studied: Uniform statistical convergence of sequence of functions, statistical epi-limit of compound of sequence of functions, statistical epi-limit of the sum of sequence of functions, the property of epi-limit function if the sequence of functions are lower semi-continuous and the convexity of epi-limit function if each function in the sequence is convex.

Özet

Bu çalışmada, istatistiksel epi-yakınsaklığın sonraki çalışmalarda daha verimli kullanılabilmesi için bazı temel özelliklere yer verildi. Bir fonksiyon dizisinin düzgün istatistiksel yakınsaklık durumu, fonksiyon dizilerinin bileşkesinin istatistiksel epi-limiti, fonksiyon dizilerinin toplamının istatistiksel epi-limiti, fonksiyon dizisinin alttan yarı sürekli olması halinde epi-limit fonksiyonunun özelliği ve fonksiyon dizisindeki her bir fonksiyonun konveks olması halinde epi-limit fonksiyonunun konveksliği gibi durumlar çalışıldı.

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Cite This Article

Tortop, Ş. (2020). Basic Properties of Statistical Epi-Convergence. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, Cilt: 20 Sayı: 6, 968–974. https://doi.org/10.35414/akufemubid.819410

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