Basic Properties of Statistical Epi-Convergence

Year 2020, , 968 - 974, 31.12.2020

Şükrü Tortop

https://doi.org/10.35414/akufemubid.819410

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.

Keywords

Epi-convergence, Statistical Convergence, Epigraph, Sequence of Functions

İstatistiksel Epi-Yakınsaklık ile İlgili Temel Özellikler

Abstract

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.

Keywords

Epi-Yakınsaklık, İstatistiksel Yakınsaklık, Epigraf, Fonksiyon Dizileri

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