scholarly journals Geometric Inequalities for Plane Convex Bodies

1979 ◽  
Vol 22 (1) ◽  
pp. 9-16 ◽  
Author(s):  
G. D. Chakerian
Keyword(s):  
Euclidean Plane ◽  
Compact Convex ◽  
Convex Bodies ◽  
Plane Convex ◽  
Left Hand ◽  
Supporting Line ◽  
Plane Convex Body ◽  
The Right ◽  
Derivatives Of ◽  
Plane Convex Bodies

In what follows we shall mean by a plane convex body K a compact convex subset of the Euclidean plane having nonempty interior. We shall denote by h (K, θ) the supporting function of K restricted to the unit circle. This measures the signed distances from the origin to the supporting line of K with outward normal (cos θ, sin θ). The right hand and left hand derivatives of h (K, θ) exist everywhere and are equal except on a countable set.

scholarly journals On the relative distances of six points in a plane convex body

2005 ◽  
Vol 42 (3) ◽  
pp. 253-264
Author(s):  
Károly Böröczky ◽  
Zsolt Lángi
Keyword(s):  
Convex Body ◽  
Upper Bound ◽  
Euclidean Distance ◽  
Euclidean Plane ◽  
Relative Distance ◽  
Plane Convex ◽  
Euclidean Length ◽  
Plane Convex Body

Let C be a convex body in the Euclidean plane. By the relative distance of points p and q we mean the ratio of the Euclidean distance of p and q to the half of the Euclidean length of a longest chord of C parallel to pq. In this note we find the least upper bound of the minimum pairwise relative distance of six points in a plane convex body.

Decomposing plane convex bodies

1972 ◽  
Vol 23 (1) ◽  
pp. 534-536 ◽  
Author(s):  
Walter Meyer
Keyword(s):  
Convex Bodies ◽  
Plane Convex ◽  
Plane Convex Bodies

scholarly journals ASYMPTOTIC INTEGRATION OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH INTEGRODIFFERENTIAL RIGHT-HAND SIDE

2015 ◽  
Vol 20 (4) ◽  
pp. 471-489 ◽  
Author(s):  
Milan Medved ◽  
Michal Pospisil
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Asymptotic Integration ◽  
Fractional Integrals ◽  
Left Hand ◽  
Right Hand ◽  
Fractional Differential ◽  
The Right ◽  
Derivatives Of ◽  
Fractional Orders

In this paper we deal with the problem of asymptotic integration of a class of fractional differential equations of the Caputo type. The left-hand side of such type of equation is the Caputo derivative of the fractional order r ∈ (n − 1, n) of the solution, and the right-hand side depends not only on ordinary derivatives up to order n − 1 but also on the Caputo derivatives of fractional orders 0 < r 1 < · · · < r m < r, and the Riemann–Liouville fractional integrals of positive orders. We give some conditions under which for any global solution x(t) of the equation, there is a constant c ∈ R such that x(t) = ctR + o(tR) as t → ∞, where R = max{n − 1, r m }.

scholarly journals Upper bounds for the perimeter of plane convex bodies

2013 ◽  
Vol 142 (2) ◽  
pp. 366-383 ◽  
Author(s):  
Alexey Glazyrin ◽  
Filip Morić
Keyword(s):  
Convex Bodies ◽  
Upper Bounds ◽  
Plane Convex ◽  
Plane Convex Bodies
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