Almost convex functions

Almost Convex Functions: Conjugacy and Duality

We prove that the formulae of the conjugates of the precomposition with a linear operator, of the sum of finitely many functions and of the sum between a function and the precomposition of another one with a linear operator hold even when the convexity assumptions are replaced by almost convexity or nearly convexity. We also show that the duality statements due to Fenchel hold when the function...

Fixed Point Theory for Almost Convex Functions

A General Theory of Almost Convex Functions

Let ∆m = {(t0, . . . , tm) ∈ Rm+1 : ti ≥ 0, ∑m i=0 ti = 1} be the standard m-dimensional simplex and let ∅ = S ⊂ ⋃∞ m=1 ∆m. Then a function h : C → R with domain a convex set in a real vector space is S-almost convex iff for all (t0, . . . , tm) ∈ S and x0, . . . , xm ∈ C the inequality h(t0x0 + · · ·+ tmxm) ≤ 1 + t0h(x0) + · · ·+ tmh(xm) holds. A detailed study of the properties of S-almost co...

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...

JENSEN’S INEQUALITY FOR GG-CONVEX FUNCTIONS

In this paper, we obtain Jensen’s inequality for GG-convex functions. Also, we get in- equalities alike to Hermite-Hadamard inequality for GG-convex functions. Some examples are given.