Displaying similar documents to “Delta-convex mappings between Banach spaces and applications”

An intersection theorem for set-valued mappings

Ravi P. Agarwal, Mircea Balaj, Donal O'Regan (2013)

Applications of Mathematics

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Given a nonempty convex set X in a locally convex Hausdorff topological vector space, a nonempty set Y and two set-valued mappings T : X ⇉ X , S : Y ⇉ X we prove that under suitable conditions one can find an x ∈ X which is simultaneously a fixed point for T and a common point for the family of values of S . Applying our intersection theorem we establish a common fixed point theorem, a saddle point theorem, as well as existence results for the solutions of some equilibrium and complementarity problems. ...

k-convexity in several complex variables

Hidetaka Hamada, Gabriela Kohr (2002)

Annales Polonici Mathematici

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We define and investigate the notion of k-convexity in the sense of Mejia-Minda for domains in ℂⁿ and also that of k-convex mappings on the Euclidean unit ball.

A d.c. C 1 function need not be difference of convex C 1 functions

David Pavlica (2005)

Commentationes Mathematicae Universitatis Carolinae

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In [2] a delta convex function on ℝ 2 is constructed which is strictly differentiable at 0 but it is not representable as a difference of two convex function of this property. We improve this result by constructing a delta convex function of class C 1 ( ℝ 2 ) which cannot be represented as a difference of two convex functions differentiable at 0. Further we give an example of a delta convex function differentiable everywhere which is not strictly differentiable at 0.