scholarly journals ISOPERIMETRIC INEQUALITIES FOR Lp GEOMINIMAL SURFACE AREA

2011 ◽  
Vol 53 (3) ◽  
pp. 717-726 ◽  
Author(s):  
BAOCHENG ZHU ◽  
NI LI ◽  
JIAZU ZHOU
Keyword(s):  
Convex Body ◽  
Surface Area ◽  
Type Inequality ◽  
Isoperimetric Inequalities ◽  
Surface Areas ◽  
Cyclic Inequality ◽  
Geominimal Surface Area

AbstractIn this paper, we establish a number of Lp-affine isoperimetric inequalities for Lp-geominimal surface area. In particular, we obtain a Blaschke–Santaló type inequality and a cyclic inequality between different Lp-geominimal surface areas of a convex body.

On a cyclic inequality

1973 ◽  
Vol 4 (2-3) ◽  
pp. 163-168 ◽  
Author(s):  
Á. Elbert
Keyword(s):  
Cyclic Inequality

scholarly journals On an Extension of Shapiro's Cyclic Inequality

2009 ◽  
Vol 2009 (1) ◽  
pp. 491576
Author(s):  
NguyenMinh Tuan ◽  
LeQuy Thuong
Keyword(s):  
Cyclic Inequality

scholarly journals Cyclic Inequality Forms with Power 1/2,1/3

2017 ◽  
Vol 33 (3) ◽  
Author(s):  
Quốc Phạm Văn
Keyword(s):  
Real Numbers ◽  
Positive Real ◽  
Cyclic Inequality

The purpose of this paper is to establish inequalities between two terms \begin{equation*} F =\sum_{i=1}^{n}\sqrt{ax_{i}^{2}+bx_{i}x_{i+1}+cx_{i+1}^{2}+dx_i+ex_{i+1}+d }; \end{equation*} \begin{equation*} G =\sum_{i=1}^{n}\sqrt[3]{ax_{i}^{3}+bx_{i}^{2}x_{i+1}+cx_{i}x_{i+1}^{2}+dx_{i+1}^{3}}, \end{equation*} and $\sum_{i=1}^{n}x_{i}$ for a sequence of cyclic positive real numbers $ (x_{i})_{i=1}^{n+1}$ with $x_{n+1}=x_{1}$. The results depends on the sign of expressions containing the coefficients $a,b,c,d$. The general case for $F$ is also investigated.

scholarly journals A Cyclic Inequality and an Extension of it. II

1962 ◽  
Vol 13 (2) ◽  
pp. 143-152 ◽  
Author(s):  
P. H. Diananda
Keyword(s):  
Real Numbers ◽  
Positive Real ◽  
Cyclic Inequality ◽  
Image Position ◽  
Positive Integers

Throughout this paper, unless otherwise stated, n and L stand for positive integers and α, t, x, x1, x2, … for positive real numbers. Letwhereand

26.—On Shapiro's Cyclic Inequality

1976 ◽  
Vol 75 (4) ◽  
pp. 333-338 ◽  
Author(s):  
P. J. Bushell ◽  
A. H. Craven
Keyword(s):  
Numerical Analysis ◽  
Elementary Proof ◽  
Negative Numbers ◽  
Counter Example ◽  
Cyclic Inequality

SynopsisThe inequality, for suitable sets of non-negative numbers x1, x2, …, xn,is undecided in the cases n = 11, 12, 13, 15, 17, 19, 21 and 23. In this note we present the results of numerical analysis supporting the conjecture that the inequality is valid in these cases. A new counter–example for n = 25 and a new elementary proof when n = 7 are given.

scholarly journals On Shapiro’s cyclic inequality for $N=13$

1985 ◽  
Vol 45 (171) ◽  
pp. 199-199
Author(s):  
B. A. Troesch
Keyword(s):  
Cyclic Inequality

scholarly journals The Cyclic Inequality of N.P. Korneichuk and it’s generalization

2019 ◽  
Author(s):  
T. V. Nakonechnaya
Keyword(s):  
Modulus Of Continuity ◽  
Independent Interest ◽  
Independent Variables ◽  
Cyclic Inequality

In this paper there is given a generalization of well-known cyclic inequality of N.P. Korneichuk on the case of n independent variables. This result is of independent interest and can be used to obtain estimated results of splines-approximation in classes with bounded modulus of continuity.

scholarly journals The validity of Shapiro’s cyclic inequality

1989 ◽  
Vol 53 (188) ◽  
pp. 657-657
Author(s):  
B. A. Troesch
Keyword(s):  
Cyclic Inequality
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