Displaying similar documents to “Extremum conditions for nonlinear functions on convex sets”

On co-ordinated quasi-convex functions

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

Czechoslovak Mathematical Journal

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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...

Drop property on locally convex spaces

Ignacio Monterde, Vicente Montesinos (2008)

Studia Mathematica

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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 weak drop property and quasi-weak drop property

J. H. Qiu (2003)

Studia Mathematica

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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...