Contemporary Mathematics Bounds on the Non-convexity of Ranges of Vector Measures with Atoms
نویسندگان
چکیده
Upper bounds are given for the distance between the range, matrix range and partition range of a vector measure to the respective convex hulls of these ranges. The bounds are speciied in terms of the maximum atom size, and generalize convexity results of Lyapounov (1940) and Dvoretzky, Wald and Wolfowitz (1951). Applications are given to the bisection problem, the "problem of the Nile", and fair division problems.
منابع مشابه
Hölder continuity of solution maps to a parametric weak vector equilibrium problem
In this paper, by using a new concept of strong convexity, we obtain sufficient conditions for Holder continuity of the solution mapping for a parametric weak vector equilibrium problem in the case where the solution mapping is a general set-valued one. Without strong monotonicity assumptions, the Holder continuity for solution maps to parametric weak vector optimization problems is discussed.
متن کاملSome existence results for generalized vector quasi-equilibrium problems
In this paper, we introduce and study a class of generalized vector quasi-equilibrium problem, which includes many vector equilibrium problems, equilibrium problems, vector variational inequalities and variational inequalities as special cases. Using one person game theorems, the concept of escaping sequences and without convexity assumptions, we prove some existence results for ...
متن کاملPseudoconvex Multiobjective Continuous-time Problems and Vector Variational Inequalities
In this paper, the concept of pseudoconvexity and quasiconvexity for continuous~-time functions are studied and an equivalence condition for pseudoconvexity is obtained. Moreover, under pseudoconvexity assumptions, some relationships between Minty and Stampacchia vector variational inequalities and continuous-time programming problems are presented. Finally, some characterizations of the soluti...
متن کاملOn Maximal Ranges of Vector Measures for Subsets and Purification of Transition Probabilities
Consider a measurable space with an atomless finite vector measure. This measure defines a mapping of the σ-field into an Euclidean space. According to the Lyapunov convexity theorem, the range of this mapping is a convex compactum. Similar ranges are also defined for measurable subsets of the space. Two subsets with the same vector measure may have different ranges. We investigate the question...
متن کاملThe convexity of the integral operator on the class of the integral operator on the class B(mu,alpha)
In this paper, we study the convexity of the integral operator
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007