Let 2 be a binary relation on R’!+. The convexed relation 2 is defined by xky iff Vz[y~conv{w:w~z}]*[x~conv{w:w~z)] [see Hildenbrand (1974)]. Starr (1969), first formally presented this relation, which was used by him and by others in equilibrium analysis of markets with non-convex preference relations [see for example Shaked (1976)]. The question arises which properties of the unconvexed relat...

In this paper, we introduce and study a class of generalized symmetric vector quasi-equilibrium problems in abstract convex spaces. By virtue of the properties of Γ-convex and KC-map, we give some sufficient conditions to guarantee the existence of solutions for the generalized symmetric vector quasi-equilibrium problems in abstract convex spaces. As application, we show an existence theorem of...

In this paper we present an algorithm of quasi-linear complexity for exactly calculating the infimal convolution of convex quadratic functions. The algorithm exactly and simultaneously solves a separable uniparametric family of quadratic programming problems resulting from varying the equality constraint.

The core objective of this article is to introduce and study new classes of α-quasi-convex functions in conic regions. Various interesting properties such as integral representation, sufficiency criteria, inclusion results and the effect of certain integral operators on these classes has also been examined.

E. A. Elrifai, H. E. Darwish, and A. R. Ahmed Faculty of Science, Mansoura University, Mansoura 35516, Egypt Correspondence should be addressed to H. E. Darwish, [email protected] Received 25 March 2010; Accepted 14 July 2010 Academic Editor: Ram N. Mohapatra Copyright q 2010 E. A. Elrifai et al. This is an open access article distributed under the Creative Commons Attribution License, which...

This paper proposes a method based on linear programming techniques to treat quasi-concave and non-concave fuzzy multi-objective programming (FMOP) problems. The proposed method initially presents a piecewise linear expression to interpreting a quasi-concave membership function. Then we 7nd the convex-type break points and transform all quasiconcave membership functions into concave functions. ...

We show that for even quasi-concave objective functions the worst-case distribution, with respect to a family of unimodal distributions, of a stochastic programming problem is a uniform distribution. This extends the so-called “Uniformity Principle” of Barmish and Lagoa (1997) where the objective function is the indicator function of a convex symmetric set.

In this paper, L-convex ?*-remotehood system is introduced and some characterizations of both L-convexity remotehood are obtained. Further, ?*-remote mapping presented its properties investigated. Based on this, quasi-uniformity quasiuniformity preserving introduced. It proved that quasi-uniform space Lconvex mutually induced. addition, the category spaces can be embedded into spaces.