in this paper we establish several polynomials similar to bernstein's polynomials and several refinements of  hermite-hadamard inequality for convex functions.

In this paper, the problem under consideration is multiobjective non-linear fractional programming problem involving semilocally convex and related functions. We have discussed the interrelation between the solution sets involving properly efficient solutions of multiobjective fractional programming and corresponding scalar fractional programming problem. Necessary and sufficient optimality...

Let $\mathcal{P}_n$ be the convex hull in $\mathbb{R}^n$ of all parking functions length $n$. Stanley found number vertices and facets $\mathcal{P}_n$. Building upon these results, we determine faces arbitrary dimension, volume, integer points

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.

In discrete convex analysis, the scaling and proximity properties for the class of L-convex functions were established more than a decade ago and have been used to design efficient minimization algorithms. For the larger class of integrally convex functions of n variables, we show here that the scaling property only holds when n ≤ 2, while a proximity theorem can be established for any n, but o...

Using the notion of eta-convex functions as generalization of convex functions, we estimate the difference between the middle and right terms in Hermite-Hadamard-Fejer inequality for differentiable mappings. Also as an application we give an error estimate for midpoint formula.

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...