Ali Reza Sattarzadeh - Department of Mathematics, Kerman Graduate University of Advanced Technology, Kerman, Iran.
Hossein Mohebi - Shahid Bahonar University of Kerman

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 engineering problems.

Spectral function, Proximal average, Moreau envelope, Infimal convolution