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Remarks on some variants of minimal point theorem and Ekeland variational principle with applications

Meghea Irina, Stamin Cristina Stefania

Demonstratio Mathematica

2022

Vol. 55, nr 1

354--379

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.

Set-valued minimax fractional programming problems under -cone arcwise connectedness

Das Koushik

Control and Cybernetics

2022

Vol. 51, No. 1

43--69

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.

Functions preserving a cone preorder and their duals

Otachel Z.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2005

Vol. 45, [Z] 2

171--180

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.

Linearly additive random fields with independent increments on time like curves

Takenaka S.

Probability and Mathematical Statistics

2003

Vol. 23, Fasc. 1

1--5

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∗.

On infinite dimensional generalization of Yan's theorem

Noori F., Mayahi-Al A.

Demonstratio Mathematica

2000

Vol. 33, nr 4

831-834