scholarly journals A generalization of Jung's theorem

1992 ◽  
Vol 42 (2) ◽  
Author(s):  
M. Henk
Keyword(s):  
Jung’S Theorem

scholarly journals Jung’s Theorem Applied in Nuclear Track Methodology

2012 ◽  
Vol 6 (1) ◽  
pp. 51-55
Author(s):  
G. Chacin ◽  
◽  
L. Sajo-Bohus ◽  
J.J. Rojas Hancco ◽  
G. Espinosa ◽  
...  
Keyword(s):  
Jung’S Theorem

AN EXTENSION OF JUNG'S THEOREM

1991 ◽  
Vol 42 (1) ◽  
pp. 209-212
Author(s):  
P.R. SCOTT
Keyword(s):  
Jung’S Theorem

scholarly journals Combinatorial Generalizations of Jung’s Theorem

2013 ◽  
Vol 49 (3) ◽  
pp. 478-484
Author(s):  
Arseniy V. Akopyan
Keyword(s):  
Jung’S Theorem

scholarly journals Stability of Pexider Equations on Semigroup with No Neutral Element

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Jaeyoung Chung
Keyword(s):  
Banach Space ◽  
Closed Form ◽  
Direct Consequence ◽  
Neutral Element ◽  
Complex Numbers ◽  
Ulam Stability ◽  
Exponential Equation ◽  
Pexider Equation ◽  
Pexider Equations ◽  
Jung’S Theorem

LetSbe a commutative semigroup with no neutral element,Ya Banach space, andℂthe set of complex numbers. In this paper we prove the Hyers-Ulam stability for Pexider equationfx+y-gx-h(y)≤ϵfor allx,y∈S, wheref,g,h:S→Y. Using Jung’s theorem we obtain a better bound than that usually obtained. Also, generalizing the result of Baker (1980) we prove the superstability for Pexider-exponential equationft+s-gth(s)≤ϵfor allt,s∈S, wheref,g,h:S→ℂ. As a direct consequence of the result we also obtain the general solutions of the Pexider-exponential equationft+s=gth(s)for allt,s∈S, a closed form of which is not yet known.

An extension of Jung’s theorem

1985 ◽  
Vol 50 (3) ◽  
pp. 169-180 ◽  
Author(s):  
B. V. Dekster
Keyword(s):  
Jung’S Theorem

scholarly journals Geometrical Bounds for Variance and Recentered Moments

2021 ◽  
Author(s):  
Tongseok Lim ◽  
Robert J. McCann
Keyword(s):  
Linear Programming ◽  
Symmetry Breaking ◽  
Random Vector ◽  
Mass Formula ◽  
Convex Duality ◽  
Probability Measures ◽  
Infinite Dimensional ◽  
Dynamics Modelling ◽  
The Mean ◽  
Jung’S Theorem

We bound the variance and other moments of a random vector based on the range of its realizations, thus generalizing inequalities of Popoviciu and of Bhatia and Davis concerning measures on the line to several dimensions. This is done using convex duality and (infinite-dimensional) linear programming. The following consequence of our bounds exhibits symmetry breaking, provides a new proof of Jung’s theorem, and turns out to have applications to the aggregation dynamics modelling attractive–repulsive interactions: among probability measures on [Formula: see text] whose support has diameter at most [Formula: see text], we show that the variance around the mean is maximized precisely by those measures that assign mass [Formula: see text] to each vertex of a standard simplex. For [Formula: see text], the [Formula: see text] th moment—optimally centered—is maximized by the same measures among those satisfying the diameter constraint.

Jung's theorem for a pair of Minkowski spaces

2006 ◽  
Vol 6 (4) ◽  
Author(s):  
Vladimir Boltyanski ◽  
Horst Martini
Keyword(s):  
Minkowski Spaces ◽  
Jung’S Theorem
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