Minimal Pairs Representing Selections of Four Linear Functions in R
نویسندگان
چکیده
In this paper we investigate minimal pairs of continuous selections of four linear functions in R3. Our purpose is to find minimal pairs of compact convex sets (polytops) which represent all 166 (see [2]) continuous selections in CS(y1, y2, y3,− ∑3 i=1 yi) in R 3. We find that these 166 selections are represented by 16 essentialy different minimal pairs which were studied in [5], [9]. Three out of 16 cases are minimal pairs that are not unique minimal representations in their own quotient classes. One of these quotient classes was already studied in [5], [10], [15].
منابع مشابه
Preclosure operator and its applications in general topology
In this paper, we show that a pointwise symmetric pre-isotonic preclosure function is uniquely determined the pairs of sets it separates. We then show that when the preclosure function of the domain is pre-isotonic and the pre-closure function of the codomain is pre-isotonic and pointwise-pre-symmetric, functions which separate only those pairs of sets which are already separated are precontinu...
متن کاملUnique common coupled fixed point theorem for four maps in $S_b$-metric spaces
In this paper we prove a unique common coupled fixed point theorem for two pairs of $w$-compatible mappings in $S_b$-metric spaces satisfying a contrctive type condition. We furnish an example to support our main theorem. We also give a corollary for Junck type maps.
متن کاملDeveloping a Minimal Pairs’ Package for Persian-speaking Children: A Preliminary Study
Objectives: Different treatment approaches have been introduced for children with Speech Sound Disorders (SSD). Minimal pair intervention, Metaphon therapy, and parents and children together approach as linguistically-based approaches are routinely utilized in this population and both of them shared minimal pairs as a common component. The purpose of the current study was to develop and investi...
متن کاملConcerning the frame of minimal prime ideals of pointfree function rings
Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of continuous real-valued functions on $L$. We study the frame $mathfrak{O}(Min(mathcal{R}L))$ of minimal prime ideals of $mathcal{R}L$ in relation to $beta L$. For $Iinbeta L$, denote by $textit{textbf{O}}^I$ the ideal ${alphainmathcal{R}Lmidcozalphain I}$ of $mathcal{R}L$. We show that sending $I$ to the set of minimal prime ...
متن کاملGeneralized multivalued $F$-contractions on non-complete metric spaces
In this paper, we explain a new generalized contractive condition for multivalued mappings and prove a fixed point theorem in metric spaces (not necessary complete) which extends some well-known results in the literature. Finally, as an application, we prove that a multivalued function satisfying a general linear functional inclusion admits a unique selection fulfilling the corresp...
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 2001