## On a Classical Review of the Fundamental Hahn-Banach Extension Result in Polynomial and Dirichlet Problem

Eziokwu, C. Emmanuel *

Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria.

Ekwoma Hannah

Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria.

*Author to whom correspondence should be addressed.

### Abstract

This paper reviews the Hahn-Banach theorem as an efficient development for functional extension in Banach spaces prior to other subsequent results for extension even in topology and functional analysis. This reviews that the Hahn-Banach result basically portrays the extent that the values of a linear functional could be pre-assigned and in this work, one considers a mathematical object specified on a subset of a given set X in a manner in which features of the objects is retained and extended as in section one below. In section two we have the fundamentals of the Hahn-Banach results as precisely considered as results and sub results. These then motivated the basis of this research while some applications were fully discussed in section three.

Keywords: Hahn-Banach extension result, normed linear space, linear function, space of polynomial, dirichlet problem

**How to Cite**

*Asian Journal of Pure and Applied Mathematics*,

*4*(1), 341–351. Retrieved from https://globalpresshub.com/index.php/AJPAM/article/view/1584

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