scholarly journals Measure of non-compactness and multivalued mappings in complete metric topological vector spaces

1985 ◽  
Vol 108 (2) ◽  
pp. 403-408 ◽  
Author(s):  
Charles Horvath
Keyword(s):  
Vector Spaces ◽  
Multivalued Mappings ◽  
Topological Vector Spaces

scholarly journals Existence Results for Strong Mixed Vector Equilibrium Problem for Multivalued Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Adem Kılıçman ◽  
Rais Ahmad ◽  
Mijanur Rahaman
Keyword(s):  
Equilibrium Problem ◽  
Existence Results ◽  
Vector Equilibrium Problem ◽  
Vector Spaces ◽  
Multivalued Mappings ◽  
Topological Vector Spaces ◽  
Fan Theorem ◽  
Special Cases ◽  
Vector Equilibrium ◽  
Generalized Pseudomonotonicity

We consider a strong mixed vector equilibrium problem in topological vector spaces. Using generalized Fan-Browder fixed point theorem (Takahashi 1976) and generalized pseudomonotonicity for multivalued mappings, we provide some existence results for strong mixed vector equilibrium problem without using KKM-Fan theorem. The results in this paper generalize, improve, extend, and unify some existence results in the literature. Some special cases are discussed and an example is constructed.

scholarly journals Topological Quasilinear Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Yılmaz Yılmaz ◽  
Sümeyye Çakan ◽  
Şahika Aytekin
Keyword(s):  
Functional Analysis ◽  
Linear Functional ◽  
Vector Spaces ◽  
Multivalued Mappings ◽  
Linear Spaces ◽  
Localization Principle ◽  
Topological Vector Spaces

We introduce, in this work, the notion of topological quasilinear spaces as a generalization of the notion of normed quasilinear spaces defined by Aseev (1986). He introduced a kind of the concept of a quasilinear spaces both including a classical linear spaces and also nonlinear spaces of subsets and multivalued mappings. Further, Aseev presented some basic quasilinear counterpart of linear functional analysis by introducing the notions of norm and bounded quasilinear operators and functionals. Our investigations show that translation may destroy the property of being a neighborhood of a set in topological quasilinear spaces in contrast to the situation in topological vector spaces. Thus, we prove that any topological quasilinear space may not satisfy the localization principle of topological vector spaces.

scholarly journals Existence Results for Generalized Vector Equilibrium Problems with Multivalued Mappings via KKM Theory

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
A. P. Farajzadeh ◽  
A. Amini-Harandi ◽  
D. O'Regan
Keyword(s):  
Equilibrium Problems ◽  
Sufficient Conditions ◽  
Vector Spaces ◽  
Multivalued Mappings ◽  
Vector Equilibrium Problems ◽  
Solution Sets ◽  
Topological Vector Spaces ◽  
Set Valued Mapping ◽  
Generalized Vector Equilibrium Problems ◽  
Vector Equilibrium

We first define upper sign continuity for a set-valued mapping and then we consider two types of generalized vector equilibrium problems in topological vector spaces and provide sufficient conditions under which the solution sets are nonempty and compact. Finally, we give an application of our main results. The paper generalizes and improves results obtained by Fang and Huang in (2005).

Finite dimensional locally convex cones

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5111-5116
Author(s):  
Davood Ayaseha
Keyword(s):  
Finite Dimension ◽  
Convex Cones ◽  
Vector Spaces ◽  
Topological Vector Spaces ◽  
Euclidean Topology ◽  
Finite Dimensional ◽  
Dimensional Cone ◽  
Locally Convex Cones ◽  
Locally Convex ◽  
Special Case

We study the locally convex cones which have finite dimension. We introduce the Euclidean convex quasiuniform structure on a finite dimensional cone. In special case of finite dimensional locally convex topological vector spaces, the symmetric topology induced by the Euclidean convex quasiuniform structure reduces to the known concept of Euclidean topology. We prove that the dual of a finite dimensional cone endowed with the Euclidean convex quasiuniform structure is identical with it?s algebraic dual.

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