In this paper, new Hermite-Hadamard type inequalities for coordinated convex and co-ordinated quasi convex functions are proved in a unique way. These results generalize many results proved in earlier works for these classes of functions. Finally, applications of our results are given to estimate the product of moments of two independent continuous random variables.

We introduce marginal worth vectors and quasi-supermodular games on convex geometries. Furthermore, we study some properties of the minimal marginal operator and the maximal marginal operator on the space of the games on convex geometries. 1991 Mathematics Subject Classi...cation: 90D12

This paper is concerned with the existence of minimizers for functionals having a double-well integrand with affine boundary conditions. Such functionals are related to the so-called Kohn-Strang functional which arises in optimal shape design problems in electrostatics or elasticity. They are known to be not quasi-convex, and therefore existence of minimizers is, in general, guaranteed only for...

The goal of this paper is to introduce the approximated convex envelope of a function and to estimate how it differs from its convex envelope. Such a problem arises in various physical situations where the function considered is some energy that has to be minimized.This study is a first step toward understanding how to approximate the quasi-convex envelope of a function. The importance of this ...

We introduce a wide subclass F(X,ω) of quasi-plurisubharmonic functions in a compact Kähler manifold, on which the complex Monge-Ampère operator is well-defined and the convergence theorem is valid. We also prove that F(X,ω) is a convex cone and includes all quasi-plurisubharmonic functions which are in the Cegrell class.

The aim of this paper is to prove strong and △-convergence theorems of modified S-iterative scheme for asymptotically quasi-nonexpansive mapping in hyperbolic spaces. The results obtained generalize several results of uniformly convex Banach spaces and CAT(0) spaces. KeywordsHyperbolic space, fixed point, asymptotically quasi nonexpansive mapping, strong convergence, △-convergence.

We prove the weak and strong convergence of the implicit iterative process to a common fixed point of an asymptotically quasi-I-nonexpansive mapping T and an asymptotically quasi-nonexpansive mapping I, defined on a nonempty closed convex subset of a Banach space.

In this paper, we introduce several types of correspondences: weakly naturally quasiconvex, *-weakly naturally quasiconvex, weakly biconvex and correspondences with *–weakly convex graph and we prove some fixed point theorems for these kinds of correspondences. As a consequence, using a version of W.K. Kim’s quasi-point theorem, we obtain the existence of equilibria for a quasi-game.

We prove, for any n, that there is a closed connected orientable surface S so that the hyperbolic space H almost-isometrically embeds into the Teichmüller space of S, with quasi-convex image lying in the thick part. As a consequence, H quasi-isometrically embeds in the curve complex of S.

*Correspondence: [email protected] 1Department of Mathematics, Hebei North University, Zhangjiakou, 075000, China Full list of author information is available at the end of the article Abstract The purpose of this article is to establish a kind of non-convex hybrid iteration algorithms and to prove relevant strong convergence theorems of common fixed points for a uniformly closed asymptotica...