The goal of multi-class classification problem is to find a discriminant function that minimizes the expectation of 0-1 loss function. However, minimizing 0-1 loss directly is often computationally intractable and practical algorithms are usually based on convex relaxations of 0-1 loss, say Φ, which is called the surrogate loss. In many applications, the covariates are either not available dire...

Restricted-orientation convexity (O-convexity) is the study of geometric objects whose intersections with lines from some xed set O of orientations are empty or connected. The notion of O-convexity generalizes standard convexity, as well as several other types of nontraditional convexity. We introduce and study O-halfspaces, which are analogs of standard halfspaces in the theory of O-convexity,...

Making use of the generalized hypergeometric functions, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients and obtain coefficient estimates, extreme points, the radii of close-to-convexity, starlikeness and convexity, and neighborhood results for the class TSm α, β, γ . In particular, we obtain integral means ineq...

In this paper we extend some theorems published lately on the relationship between convexity/concavity, and subadditivity/superadditivity. We also generalize inequalities of compound functions that refine Minkowski inequality.

We establish the preserving log-convexity property for the generalized Pascal triangles. It is an extension of a result of H. Davenport and G. Pólya “On the product of two power series”, who proved that the binomial convolution of two log-convex sequences is log-convex.

Marshal Ash [3] introduced the concept of (σ, τ) differentiable functions and studied the Riemann generalized derivatives In this article we study the convexity and monotonicity of (σ, τ) differentiable functions, using results by Hincin, Humke and Laczkovich, and using the Riemann generalized derivative. We give conditions such that the classic properties of differentiable functions hold also ...

In this paper, we prove that each of the following functions is convex on R: f(t) = wN(AtXA1?t ? A1?tXAt), g(t) wN(AtXA1?t), and h(t) wN(AtXAt) where A > 0, X Mn N(.) a unitarily invariant norm onMn. Consequently, answer positively question concerning convexity function t w(AtXAt) proposed by in (2018). We provide some generalizations extensions wN(.) using Kwong functions. More precisely, w...