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.

The present knowledge about L-convex and M-convex functions are surveyed on the basis of [27].

Extending and improving some recent results of Hantoute, López, and Zălinescu and others, we provide characterization conditions for subdifferential formulas to hold for the supremum function of a family of convex functions on a real locally convex space.

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 ...

insisting that the equality sign holds when k = n. Here, x[X] > • • • > x[n] are the xt arranged in decreasing order and, similarly, y[X] > • • • > y[n]. If (1) is only required for the increasing (decreasing) convex functions on R then one speaks of weak sub-majorization x >, respectively). The first is equivalent to (2). Let & be an open convex subset of R...

In this paper, we introduced and investigated starlike and convex functions of order α with respect to 2(j,k)-symmetric conjugate points and coefficient inequality for function belonging to these classes are provided . Also we obtain some convolution condition for functions belonging to this class.

Let $C_0(alpha)$ denote the class of concave univalent functions defined in the open unit disk $mathbb{D}$. Each function $f in C_{0}(alpha)$ maps the unit disk $mathbb{D}$ onto the complement of an unbounded convex set. In this paper, we study the mapping properties of this class under integral operators.

In this paper, we  present a version of Favard's inequality for special case and then generalize it for the Sugeno integral in fuzzy measure space $(X,Sigma,mu)$, where $mu$ is the Lebesgue measure. We consider two cases, when our function is concave and when is convex. In addition for illustration of theorems, several examples are given.