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1
Content available remote On infinite dimensional generalization of Yan's theorem
100%
Noori F. , Mayahi-Al A.
Demonstratio Mathematica
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2000
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tom Vol. 33, nr 4
831-834
2
Content available remote Linearly additive random fields with independent increments on time like curves
100%
Takenaka S.
Probability and Mathematical Statistics
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2003
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tom Vol. 23, Fasc. 1
1--5
EN
Let V be a convex cone in Rn. A curve L = {l(t); t ∈ R+} ⊂ Rn is called a time-like curve if {l(s); s ≥ t} ⊂ l(t) + V holds for any t. A random field {X(t); t ∈ Rn} whose restriction X|L(t) = X (l(t)) on time-like curve L becomes an additive process is considered and it is characterized as a set-indexed random field on the dual cone V∗.
3
Content available remote Zero-one completely positive matrices and the A(R, S) classes
100%
Dahl G. , Haufmann T. A.
Special Matrices
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2016
|
tom 4
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nr 1
296-304
EN
A matrix of the form A = BBT where B is nonnegative is called completely positive (CP). Berman and Xu (2005) investigated a subclass of CP-matrices, called f0, 1g-completely positive matrices. We introduce a related concept and show connections between the two notions. An important relation to the so-called cut cone is established. Some results are shown for f0, 1g-completely positive matrices with given graphs, and for {0,1}-completely positive matrices constructed from the classes of (0, 1)-matrices with fixed row and column sums.
4
Content available remote Extensions of convex functionals on convex cones
100%
Ignaczak E. , Paszkiewicz A.
Applicationes Mathematicae
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1998-1999
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tom 25
|
nr 3
381-386
EN
We prove that under some topological assumptions (e.g. if M has nonempty interior in X), a convex cone M in a linear topological space X is a linear subspace if and only if each convex functional on M has a convex extension on the whole space X.
5
Content available Set-valued minimax fractional programming problems under -cone arcwise connectedness
88%
Das K.
Control and Cybernetics
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2022
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tom Vol. 51, No. 1
43--69
EN
In this paper, we consider a set-valued minimax fractional programming problem (MFP), where the objective as well as constraint maps are set-valued. We introduce the notion of ρ- cone arcwise connectedness of set-valued maps as a generalization of cone arcwise connected set-valued maps. We establish the sufficient Karush-Kuhn-Tucker (KKT) conditions for the existence of minimizers of the problem (MFP) under ρ-cone arcwise connectedness assumption. Further, we study the Mond-Weir (MWD), Wolfe (WD), and mixed (MD) types of duality models and prove the corresponding weak, strong, and converse duality theorems between the primal (MFP) and the corresponding dual problems under ρ-cone arcwise connectedness assumption.
6
Content available remote Functions preserving a cone preorder and their duals
75%
Otachel Z.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2005
|
tom Vol. 45, [Z] 2
171--180
EN
In this paper isotone functions and their dual cones are studied. Special attention is devoted to functions preserving cone preorders. This isotonicity is characterized by integral inequalities. The result yields some generators of dual cones of isotone functions. As an application a generalization of Steffensen Inequality is given.
7
Functions preserving a cone preorder and their duals
75%
Otachel Z.
Commentationes Mathematicae
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2005
|
tom 45
|
nr 2
EN
In this paper isotone functions and their dual cones are studied. Special attention is devoted to functions preserving cone preorders. This isotonicity is characterized by integral inequalities. The result yields some generators of dual cones of isotone functions. As an application a generalization of Steffensen Inequality is given.
8
Content available remote Remarks on some variants of minimal point theorem and Ekeland variational principle with applications
44%
Meghea I. , Stamin C. S.
Demonstratio Mathematica
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2022
|
tom Vol. 55, nr 1
354--379
EN
This paper presents some variants of minimal point theorem together with corresponding variants of Ekeland variational principle. In the second part of this article, there is a discussion on Ekeland variational principle and minimal point theorem relative to it in uniform spaces. The aim of these series of important results is to highlight relations between them, some improvements and specific applications.
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