we first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a banach space and next show that if the banach space is having the opial condition, then the fixed points set of such a mapping with the convex range is nonempty. in particular, we establish that if the banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...

The main purpose of this paper is to introduce the compatibility of $M$-fuzzifying topologies and $M$-fuzzifying convexities, define an $M$-fuzzifying topological convex space, and give a method to generate an $M$-fuzzifying topological convex space. Some characterizations of $M$-fuzzifying topological convex spaces are presented. Finally, the notion of $M$-fuzzifying weak topologies is obtaine...

Abstract We prove several estimates for the volume, mean width, and value of Wills functional sections convex bodies in John’s position, as well their polar bodies. These extend some well-known results position to case lower-dimensional sections, which had mainly been studied cube regular simplex. Some centrally symmetric minimal surface area are also obtained.

2 Abstract. We present a new method that allows to enumerate various classes of column-convex polygons, according to their perimeter and their area. The rst step of this method leads to a functional equation which deenes implicitly the generating function of the class under consideration. The second step consists in solving this equation. We apply systematically our method to all the usual clas...

in this paper, we define the notions of fuzzy congruence relations and fuzzy convex subalgebras on a commutative residuated lattice and we obtain some related results. in particular, we will show that there exists a one to one correspondence between the set of all fuzzy congruence relations and the set of all fuzzy convex subalgebras on a commutative residuated lattice. then we study fuzzy...

We study the inflated phase of two dimensional lattice polygons, both convex and column-convex, with fixed area A and variable perimeter, when a weight μ exp[−Jb] is associated to a polygon with perimeter t and b bends. The mean perimeter is calculated as a function of the fugacity μ and the bending rigidity J . In the limit μ → 0, the mean perimeter has the asymptotic behaviour 〈t〉/4 √ A ≃ 1−K...

Hermite-Hadamard inequality is one of the fundamental applications of convex functions in Theory of Inequality. In this paper, Hermite-Hadamard inequalities for $mathbb{B}$-convex and $mathbb{B}^{-1}$-convex functions are proven.

If a convex body K in R is contained in a convex body L of elliptic type (a curvature image), then it is known that the affine surface area of K is not larger than the affine surface area of L. We prove that the affine surface areas of K and L can only be equal if K = L. 2010 Mathematics Subject Classification: primary 52A10; secondary 53A15

Most visibility culling algorithms require convexity of occluders. Occluder synthesis algorithms attempt to construct large convex occluders inside bulky non-convex sets. Occluder fusion algorithms generate convex occluders that are contained in the umbra cast by a group of objects given an area light. In this paper we prove that convexity requirements can be shifted from the occluders to their...

We investigate the problem of finding a minimum-area container for the disjoint packing of a set of convex polygons by translations. In particular, we consider axis-parallel rectangles or arbitrary convex sets as containers. For both optimization problems which are NP-hard we develop efficient constant factor approximation algorithms.