scholarly journals On super efficiency in set-valued optimisation in locally convex spaces

2005 ◽  
Vol 71 (2) ◽  
pp. 183-192 ◽  
Author(s):  
Yihong Xu ◽  
Chuanxi Zhu
Keyword(s):  
Convex Sets ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Efficient Solutions ◽  
Separation Theorem ◽  
Topological Spaces ◽  
Locally Convex Spaces ◽  
Super Efficiency ◽  
Locally Convex ◽  
Convex Spaces

The set-valued optimisation problem with constraints is considered in the sense of super efficiency in locally convex linear topological spaces. Under the assumption of nearly cone-subconvexlikeness, by applying the separation theorem for convex sets, Kuhn-Tucker and Lagrange necessary conditions for the set-valued optimisation problem to attain its super efficient solutions are obtained. Also, Kuhn-Tucker and Lagrange sufficient conditions are derived. Finally two kinds of unconstrained programs equivalent to set-valued optimisation problems are established.

On the super efficiency in locally convex spaces

2001 ◽  
Vol 44 (6) ◽  
pp. 821-828 ◽  
Author(s):  
Fu Wantao ◽  
Cheng Yonghong
Keyword(s):  
Locally Convex Spaces ◽  
Super Efficiency ◽  
Locally Convex ◽  
Convex Spaces

scholarly journals Semiconvex spaces

1968 ◽  
Vol 9 (2) ◽  
pp. 111-118 ◽  
Author(s):  
S. O. Iyahen
Keyword(s):  
General Linear ◽  
Topological Spaces ◽  
Locally Convex Spaces ◽  
Parallel Study ◽  
Barrelled Spaces ◽  
Locally Convex ◽  
Convex Spaces

Many of the techniques and notions used to study various important theorems in locally convex spaces are not effective for general linear topological spaces. In [4], a study is made of notionsin general linear topological spaces which can be used to replace barrelled, bornological, and quasi-barrelled spaces. The present paper contains a parallel study in the context of semiconvex spaces.

scholarly journals Regularization of cylindrical processes in locally convex spaces

2020 ◽  
pp. 2050027
Author(s):  
Christian A. Fonseca-Mora
Keyword(s):  
Convex Space ◽  
Lévy Process ◽  
Sufficient Conditions ◽  
Locally Convex Space ◽  
Levy Process ◽  
Locally Convex Spaces ◽  
Locally Convex ◽  
Strong Dual ◽  
Convex Spaces

Let [Formula: see text] be a locally convex space and let [Formula: see text] denote its strong dual. In this paper, we introduce sufficient conditions for the existence of a continuous or a càdlàg [Formula: see text]-valued version to a cylindrical process defined on [Formula: see text]. Our result generalizes many other known results on the literature and their different connections will be discussed. As an application, we provide sufficient conditions for the existence of a [Formula: see text]-valued càdlàg Lévy process version to a given cylindrical Lévy process in [Formula: see text].

On B() and Br() locally convex spaces

1970 ◽  
Vol 68 (1) ◽  
pp. 95-97 ◽  
Author(s):  
L. J. Sulley
Keyword(s):  
Topological Spaces ◽  
Locally Convex Spaces ◽  
Completeness Condition ◽  
Locally Convex ◽  
Convex Spaces

1. Introduction. In his papers (2), (3) and (4), and in his book (5), Husain studied the locally convex, Hausdorff, linear topological spaces (hereafter abbreviated to l.c. spaces) which he called B() spaces and Br() spaces and which satisfy weakened forms of the B completeness and Br completeness conditions of Ptak (8). L.c. spaces satisfying another weakening of the Br completeness condition were studied by Persson in (7) and were called by him, weakly t-polar. We consider some examples in connexion with these spaces.

scholarly journals On Homomorphisms, Open Operators and their Adjoints

2001 ◽  
Vol 8 (4) ◽  
pp. 823-844
Author(s):  
D. Zarnadze
Keyword(s):  
Adjoint Operator ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Locally Convex Spaces ◽  
Necessary And Sufficient ◽  
Locally Convex ◽  
Convex Spaces

Abstract The well-known A. Grothendieck's theorem on a homomorphism between locally convex spaces is generalized to the case of topologies which are incompatible with dualities. On the basis of this theorem, necessary and sufficient conditions are obtained for a weak homomorphism (resp. its adjoint operator, resp. its double adjoint operator) to be again a homomorphism in various topologies of the initial (resp. dual, resp. bidual) spaces. Some new classes of pairs of locally convex spaces satisfying these conditions are established. The results obtained have enabled us to reveal new properties of frequently encountered homomorphisms and weakly open operators, as well as to strengthen and generalize some well-known results.

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