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...

This article deals with Hadamard inequalities for strongly s , m -convex functions using generalized Riemann–Liouville fractional integrals. Several versions of the inequality are presented; we also provide refinements many known resu...

In this paper, new classes of generalized (F,α,ρ, d)-V -type I functions are introduced for differentiable multiobjective programming problems. Based upon these generalized convex functions, sufficient optimality conditions are established. Weak, strong and strict converse duality theorems are also derived for Wolfe and Mond-Weir type multiobjective dual programs.

Various supervised inference methods can be analyzed as convex duals of the generalized maximum entropy (MaxEnt) framework. Generalized MaxEnt aims to find a distribution that maximizes an entropy function while respecting prior information represented as potential functions in miscellaneous forms of constraints and/or penalties. We extend this framework to semi-supervised learning by incorpora...

Abstract. In this paper, we introduce three new broad classes of secondorder generalized convex functions, namely, (F , b, φ, ρ, θ)-sounivex functions, (F , b, φ, ρ, θ)-pseudosounivex functions, and (F , b, φ, ρ, θ)-quasisounivex functions; formulate eight general second-order duality models; and prove appropriate duality theorems under various generalized (F , b, φ, ρ, θ)-sounivexity assumptio...

A new subclass of bi-close-to-convex functions associated with the generalized hypergeometric defined in ?={z?C:|z|<1} is introduced. The estimates for general Taylor–Maclaurin coefficients introduced are obtained by making use Faber polynomial expansions. In particular, several previous results generalized.