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