Properties of systems of n-dimensional convex sets in finite-dimensional linear spaces

1979 ◽  
Vol 25 (4) ◽  
pp. 312-320 ◽  
Author(s):  
A. G. Netrebin
Keyword(s):  
Convex Sets ◽  
Linear Spaces ◽  
Finite Dimensional

scholarly journals A new class of fractional type set-valued functions

2019 ◽  
Vol 35 (1) ◽  
pp. 79-84
Author(s):  
ALEXANDRU ORZAN ◽  
Keyword(s):  
Special Class ◽  
Convex Sets ◽  
Linear Spaces ◽  
New Class ◽  
Finite Dimensional ◽  
Affine Functions ◽  
Real Linear ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Fractional Type

The so-called ratios of affine functions, introduced by Rothblum (1985) in the framework of finite-dimensional Euclidean spaces, represent a special class of fractional type vector-valued functions, which transform convex sets into convex sets. The aim of this paper is to show that a similar convexity preserving property holds within a new class of fractional type set-valued functions, acting between any real linear spaces.

scholarly journals Convex sets in proximal relator spaces

Filomat ◽  
2016 ◽  
Vol 30 (13) ◽  
pp. 3411-3414 ◽  
Author(s):  
J.F. Peters
Keyword(s):  
Linear Space ◽  
Normed Linear Space ◽  
Convex Sets ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Finite Dimensional

This article introduces convex sets in finite-dimensional normed linear spaces equipped with a proximal relator. A proximal relator is a nonvoid family of proximity relations R? (called a proximal relator) on a nonempty set. A normed linear space endowed with R? is an extension of the Sz?z relator space. This leads to a basis for the study of the nearness of convex sets in proximal linear spaces.

Total Lattices of Convex Sets and of Linear Spaces

1948 ◽  
Vol 49 (3) ◽  
pp. 659 ◽  
Author(s):  
Walter Prenowitz
Keyword(s):  
Convex Sets ◽  
Linear Spaces

A Characterization of Finite Dimensional Convex Sets

1952 ◽  
Vol 74 (3) ◽  
pp. 683 ◽  
Author(s):  
E. G. Straus ◽  
F. A. Valentine
Keyword(s):  
Convex Sets ◽  
Finite Dimensional

Best Approximation on Convex Sets in Metric Linear Spaces

1977 ◽  
Vol 78 (1) ◽  
pp. 125-130 ◽  
Author(s):  
G. C. Ahuja ◽  
T. D. Narang ◽  
Swaran Trehan
Keyword(s):  
Best Approximation ◽  
Convex Sets ◽  
Linear Spaces
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