Exponentially Convex Functions on Hypercomplex Systems

Exponentially Convex Functions on Hypercomplex Systems

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...

Operations on M-Convex Functions on Jump Systems

A jump system is a set of integer points with an exchange property, which is a generalization of a matroid, a delta-matroid, and a base polyhedron of an integral polymatroid (or a submodular system). Recently, the concept of M-convex functions on constant-parity jump systems is introduced by Murota as a class of discrete convex functions that admit a local criterion for global minimality. M-con...

Plurisubharmonic functions on hypercomplex manifolds and HKT-geometry

A hypercomplex manifold is a manifold equipped with a triple of complex structures I, J,K satisfying the quaternionic relations. We define a quaternionic analogue of plurisubharmonic functions on hypercomplex manifolds, and interpret these functions geometrically as potentials of HKT (hyperkähler with torsion) metrics, and prove a quaternionic analogue of A.D. Aleksandrov and Chern-Levine-Niren...

On the quadratic support of strongly convex functions

In this paper, we first introduce the notion of $c$-affine functions for $c> 0$. Then we deal with some properties of strongly convex functions in real inner product spaces by using a quadratic support function at each point which is $c$-affine. Moreover, a Hyers–-Ulam stability result for strongly convex functions is shown.