Displaying similar documents to “Structure of efficient sets for strictly quasi convex objectives.”

On weak drop property and quasi-weak drop property

J. H. Qiu (2003)

Studia Mathematica

Similarity:

Every weakly sequentially compact convex set in a locally convex space has the weak drop property and every weakly compact convex set has the quasi-weak drop property. An example shows that the quasi-weak drop property is strictly weaker than the weak drop property for closed bounded convex sets in locally convex spaces (even when the spaces are quasi-complete). For closed bounded convex subsets of quasi-complete locally convex spaces, the quasi-weak drop property is equivalent to weak...

On the quasi-weak drop property

J. H. Qiu (2002)

Studia Mathematica

Similarity:

A new drop property, the quasi-weak drop property, is introduced. Using streaming sequences introduced by Rolewicz, a characterisation of the quasi-weak drop property is given for closed bounded convex sets in a Fréchet space. From this, it is shown that the quasi-weak drop property is equivalent to weak compactness. Thus a Fréchet space is reflexive if and only if every closed bounded convex set in the space has the quasi-weak drop property.

Drop property on locally convex spaces

Ignacio Monterde, Vicente Montesinos (2008)

Studia Mathematica

Similarity:

A single technique provides short proofs of some results about drop properties on locally convex spaces. It is shown that the quasi drop property is equivalent to a drop property for countably closed sets. As a byproduct, we prove that the drop and quasi drop properties are separably determined.

On co-ordinated quasi-convex functions

M. Emin Özdemir, Ahmet Ocak Akdemir, Çetin Yıldız (2012)

Czechoslovak Mathematical Journal

Similarity:

A function f : I → ℝ , where I ⊆ ℝ is an interval, is said to be a convex function on I if f ( t x + ( 1 - t ) y ) ≤ t f ( x ) + ( 1 - t ) f ( y ) holds for all x , y ∈ I and t ∈ [ 0 , 1 ] . There are several papers in the literature which discuss properties of convexity and contain integral inequalities. Furthermore, new classes of convex functions have been introduced in order to generalize the results and to obtain new estimations. We define some new classes of convex functions that we name quasi-convex, Jensen-convex, Wright-convex, Jensen-quasi-convex and Wright-quasi-convex...