The Q-convexity is a kind of convexity in the discrete plane. This notion has practically the same properties as the usual convexity: an intersection of two Qconvex sets is Q-convex, and the salient points can be defined like the extremal points. Moreover a Q-convex set is characterized by its salient point. The salient points can be generalized to any finite subset of Z2.

In the present investigation, we obtain certain sufficient conditions for a normalized analytic function f(z) defined by the Dziok–Srivastava linear operator Hm1⁄2a1 to satisfy the certain subordination. Our results extend corresponding previously known results on starlikeness, convexity, and close to convexity. 2006 Elsevier Inc. All rights reserved.

We prove the existence of free boundary minimal annuli inside suitably convex subsets of three-dimensional Riemannian manifolds with nonnegative Ricci curvature − including strictly convex domains of the Euclidean space R.

We define the notions of strong convexity and strong visibility. These notions generalize standard convexity and visibility, as well as several types of nontraditional convexity, such as iso-oriented rectangles and C-oriented polygons. We explore the properties of strong convexity and strong visibility in two and three dimensions. In particular, we establish analogs of the following properties ...

where An is the n-fold product of the σ-algebra A of subsets of a given set X , Fi,Gi, i∈ p ≡ {1,2, . . . , p}, and Hj , j ∈ q, are real-valued functions defined on An, and for each i∈ p, Gi(S) > 0 for all S∈An such that Hj(S) ≤ 0, j ∈ q. This problem was considered previously in the companion paper [7] where a survey of currently available optimality and duality results for minmax fractional s...

Convex programming involves a convex set F ⊆ R and a convex cost function c : F → R. The goal of convex programming is to find a point in F which minimizes c. In online convex programming, the convex set is known in advance, but in each step of some repeated optimization problem, one must select a point in F before seeing the cost function for that step. This can be used to model factory produc...

In this paper, we establish some Hermite-Hadamard type inequalities for function whose n-th derivatives are logarithmically convex by using Riemann-Liouville integral operator.

We study the convex combinations of $(d+1)$ generalized Pauli dynamical maps in a Hilbert space dimension $d$. For certain choices decoherence function, are noninvertible and they remain under as well. case characterized by function $(1-e^{-ct})/n$ with parameter $n$ decay factor $c$, we evaluate fraction invertible obtained upon mixing, which is found to increase superexponentially