Functions, Measures, and Equipartitioning Convex k-Fans
نویسندگان
چکیده
A k-fan in the plane is a point x ∈R2 and k halflines starting from x. There are k angular sectors σ1, . . . , σk between consecutive halflines. The k-fan is convex if every sector is convex. A (nice) probability measure μ is equipartitioned by the k-fan if μ(σi) = 1/k for every sector. One of our results: Given a nice probability measure μ and a continuous function f defined on sectors, there is a convex 5-fan equipartitioning μ with f (σ1)= f (σ2)= f (σ3).
منابع مشابه
Equipartitioning by a convex 3-fan
We show that for a given planar convex set K of positive area there exist three pairwise internally disjoint convex sets whose union is K such that they have equal area and equal perimeter. © 2009 Elsevier Inc. All rights reserved.
متن کاملEgoroff Theorem for Operator-Valued Measures in Locally Convex Cones
In this paper, we define the almost uniform convergence and the almost everywhere convergence for cone-valued functions with respect to an operator valued measure. We prove the Egoroff theorem for Pvalued functions and operator valued measure θ : R → L(P, Q), where R is a σ-ring of subsets of X≠ ∅, (P, V) is a quasi-full locally convex cone and (Q, W) is a locally ...
متن کاملHigher order close-to-convex functions associated with Attiya-Srivastava operator
In this paper, we introduce a new class$T_{k}^{s,a}[A,B,alpha ,beta ]$ of analytic functions by using a newly defined convolution operator. This class contains many known classes of analytic and univalent functions as special cases. We derived some interesting results including inclusion relationships, a radius problem and sharp coefficient bound for this class.
متن کاملFunctionally closed sets and functionally convex sets in real Banach spaces
Let $X$ be a real normed space, then $C(subseteq X)$ is functionally convex (briefly, $F$-convex), if $T(C)subseteq Bbb R $ is convex for all bounded linear transformations $Tin B(X,R)$; and $K(subseteq X)$ is functionally closed (briefly, $F$-closed), if $T(K)subseteq Bbb R $ is closed for all bounded linear transformations $Tin B(X,R)$. We improve the Krein-Milman theorem ...
متن کاملOn Hadamard and Fej'{e}r-Hadamard inequalities for Caputo $small{k}$-fractional derivatives
In this paper we will prove certain Hadamard and Fejer-Hadamard inequalities for the functions whose nth derivatives are convex by using Caputo k-fractional derivatives. These results have some relationship with inequalities for Caputo fractional derivatives.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete & Computational Geometry
دوره 49 شماره
صفحات -
تاریخ انتشار 2013