scholarly journals On the proof of the analytic form of the Hahn Banach theorem in real linear spaces

2014 ◽  
Vol 9 ◽  
pp. 1423-1426
Author(s):  
B. G. Akuchu
Keyword(s):  
Analytic Form ◽  
Linear Spaces ◽  
Banach Theorem ◽  
Real Linear

scholarly journals Semiconvex geometry

1981 ◽  
Vol 30 (4) ◽  
pp. 496-510 ◽  
Author(s):  
Joe Flood
Keyword(s):  
Algebraic Variety ◽  
Convex Sets ◽  
Convex Geometry ◽  
Algebraic Approach ◽  
Algebraic Proof ◽  
Linear Spaces ◽  
Structural Decomposition ◽  
Banach Theorem ◽  
Real Linear ◽  
Convex Subsets

AbstractSemiconvex sets are objects in the algebraic variety generated by convex subsets of real linear spaces. It is shown that the fundamental notions of convex geometry may be derived from an entirely algebraic approach, and that conceptual advantages result from applying notions derived from algebra, such as ideals, to convex sets. Some structural decomposition results for semiconvex sets are obtained. An algebraic proof of the algebraic Hahn-Banach theorem is presented.

scholarly journals A Hahn-Banach theorem for semifields

1969 ◽  
Vol 10 (1-2) ◽  
pp. 20-22 ◽  
Author(s):  
Martin Kleiber ◽  
W. J. Pervin
Keyword(s):  
Type Theorem ◽  
Linear Functionals ◽  
Linear Spaces ◽  
Banach Theorem ◽  
Real Linear

Iseki and Kasahara (see [3]) have given a Hahn-Banach type theorem for semifield-valued linear functionals on real linear spaces. We shall generalize their result by considering linear spaces over semifields.

scholarly journals Dual Spaces and Hahn-Banach Theorem

2014 ◽  
Vol 22 (1) ◽  
pp. 69-77 ◽  
Author(s):  
Keiko Narita ◽  
Noboru Endou ◽  
Yasunari Shidama
Keyword(s):  
Extension Theorem ◽  
Normed Spaces ◽  
Linear Spaces ◽  
Dual Spaces ◽  
Basic Properties ◽  
Banach Theorem ◽  
Real Linear

Summary In this article, we deal with dual spaces and the Hahn-Banach Theorem. At the first, we defined dual spaces of real linear spaces and proved related basic properties. Next, we defined dual spaces of real normed spaces. We formed the definitions based on dual spaces of real linear spaces. In addition, we proved properties of the norm about elements of dual spaces. For the proof we referred to descriptions in the article [21]. Finally, applying theorems of the second section, we proved the Hahn-Banach extension theorem in real normed spaces. We have used extensively used [17].

On the Intrinsic Core of Convex Cones in Real Linear Spaces

2021 ◽  
Vol 31 (2) ◽  
pp. 1276-1298
Author(s):  
Bahareh Khazayel ◽  
Ali Farajzadeh ◽  
Christian Günther ◽  
Christiane Tammer
Keyword(s):  
Convex Cones ◽  
Linear Spaces ◽  
Real Linear

scholarly journals Nearly directed subspaces of partially ordered linear spaces

1968 ◽  
Vol 16 (2) ◽  
pp. 135-144
Author(s):  
G. J. O. Jameson
Keyword(s):  
Linear Space ◽  
Transitive Relation ◽  
Linear Spaces ◽  
Real Linear Space ◽  
Partially Ordered ◽  
Real Linear ◽  
Image Position ◽  
Ordered Linear Spaces

Let X be a partially ordered linear space, i.e. a real linear space with a reflexive, transitive relation ≦ such that

scholarly journals ϵ-Henig Saddle Points and Duality of Set-Valued Optimization Problems in Real Linear Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhi-Ang Zhou
Keyword(s):  
Saddle Point ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Saddle Points ◽  
Linear Spaces ◽  
Equivalent Characterization ◽  
Generalized Cone Subconvexlikeness ◽  
Real Linear ◽  
The Relationship

We studyϵ-Henig saddle points and duality of set-valued optimization problems in the setting of real linear spaces. Firstly, an equivalent characterization ofϵ-Henig saddle point of the Lagrangian set-valued map is obtained. Secondly, under the assumption of the generalized cone subconvexlikeness of set-valued maps, the relationship between theϵ-Henig saddle point of the Lagrangian set-valued map and theϵ-Henig properly efficient element of the set-valued optimization problem is presented. Finally, some duality theorems are given.

scholarly journals Multilinear Operator and Its Basic Properties

2019 ◽  
Vol 27 (1) ◽  
pp. 35-45
Author(s):  
Kazuhisa Nakasho
Keyword(s):  
Algebraic Structure ◽  
Multilinear Operator ◽  
Multilinear Operators ◽  
Normed Spaces ◽  
Linear Spaces ◽  
Basic Properties ◽  
Normed Linear Spaces ◽  
Real Linear

Summary In the first chapter, the notion of multilinear operator on real linear spaces is discussed. The algebraic structure [2] of multilinear operators is introduced here. In the second chapter, the results of the first chapter are extended to the case of the normed spaces. This chapter shows that bounded multilinear operators on normed linear spaces constitute the algebraic structure. We referred to [3], [7], [5], [6] in this formalization.

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