On basic properties of convex functions and convex integrands

Legendre-type integrands and convex integral functions

In this paper, we study the properties of integral functionals induced on LE(S, μ) by closed convex functions on a Euclidean space E. We give sufficient conditions for such integral functions to be strongly rotund (well-posed). We show that in this generality functions such as the Boltzmann-Shannon entropy and the Fermi-Dirac entropy are strongly rotund. We also study convergence in measure and...

Basic Properties of Convex Polytopes

Convex polytopes are fundamental geometric objects that have been investigated since antiquity. The beauty of their theory is nowadays complemented by their importance for many other mathematical subjects, ranging from integration theory, algebraic topology, and algebraic geometry (toric varieties) to linear and combinatorial optimization. In this chapter we try to give a short introduction, pr...

Some Results on Convex Spectral Functions: I

In this paper, we give a fundamental convexity preserving for spectral functions. Indeed, we investigate infimal convolution, Moreau envelope and proximal average for convex spectral functions, and show that this properties are inherited from the properties of its corresponding convex function. This results have many applications in Applied Mathematics such as semi-definite programmings and eng...

Some Properties of Certain Subclasses of Close-to-Convex and Quasi-convex Functions with Respect to 2k-Symmetric Conjugate Points

some properties of certain subclasses of close-to-convex and quasi-convex functions with respect to 2k-symmetric conjugate points

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