Analisis Eksistensi Infimum Image Dari Fungsi Lower Semi-Continuous dari Atas

Qurratul Aini

doi:10.29303/emj.v1i1.4

Abstract

In some cases in applied mathematics, the continuous function is not used, but rather the weaker function, i.e. lower semi-continuous function from above. One of the basic properties of the function that needs to be known is the existence of the infimum value of the function image. In the case of a continuous function, the existence of infimum is assured by several assumptions, one of which is the function domain which is a closed set and the function is a bounded function. In this paper, we describe the properties that ensure the existence of infimum of the image of a lower semi-continuous function from above. Based on the results, it is found that the existence of infimum of the image of a lower semi-continuous function from above is assured in the domain which is a compact set and also assured if the function is a convex function.

Highlights

In some cases in applied mathematics, the continuous function is not used, but rather the weaker function, i.e. lower semicontinuous function from above
One of the basic properties of the function that needs to be known is the existence of the infimum value of the function image
In the case of a continuous function, the existence of infimum is assured by several assumptions, one of which is the function domain which is a closed set and the function is a bounded function

Summary

Introduction

In some cases in applied mathematics, the continuous function is not used, but rather the weaker function, i.e. lower semicontinuous function from above. Analisis Eksistensi Infimum Image Dari Fungsi Lower Semi-Continuous dari Atas Akan dianalisis sifat yang menjamin eksistensi infimum image dari fungsi lower semi-continuous dari atas. Fungsional f : X → R dikatakakan lower semi-continuous di x0 X jika untuk setiap net {x } X dengan x → x0 , berlaku : f (x0) lim f (x )

Results

Conclusion