Schur-$m$ power convexity of Cauchy means and its application

2020 ◽  
Vol 50 (5) ◽  
pp. 1859-1869
Author(s):  
Dong-Sheng Wang ◽  
Chunru Fu ◽  
Huannan Shi
Keyword(s):  
Cauchy Means

scholarly journals Characterization of the equality of Cauchy means to quasiarithmetic means

2020 ◽  
Vol 484 (1) ◽  
pp. 123700
Author(s):  
Rezső L. Lovas ◽  
Zsolt Páles ◽  
Amr Zakaria
Keyword(s):  
Quasiarithmetic Means ◽  
Cauchy Means

Multidimensional reversed Hardy type inequalities for monotone functions

2014 ◽  
Vol 07 (04) ◽  
pp. 1450055
Author(s):  
Saad Ihsan Butt ◽  
Josip Pečarić ◽  
Ivan Perić ◽  
Marjan Praljak
Keyword(s):  
Mean Value ◽  
Monotone Functions ◽  
Mean Value Theorems ◽  
Hardy Type Inequalities ◽  
Multidimensional Generalization ◽  
Exponential Convexity ◽  
Hardy Type ◽  
Cauchy Means

In this paper, we will give some multidimensional generalization of reversed Hardy type inequalities for monotone functions. Moreover, we will give n-exponential convexity, exponential convexity and related results for some functionals obtained from the differences of these inequalities. At the end we will give mean value theorems and Cauchy means for these functionals.

scholarly journals Cauchy Means of the Popoviciu Type

2009 ◽  
Vol 2009 (1) ◽  
pp. 628051
Author(s):  
Matloob Anwar ◽  
Naveed Latif ◽  
J Pečarić
Keyword(s):  
Cauchy Means

scholarly journals Invariance of the Cauchy mean-value expression with an application to the problem of representation of Cauchy means

2005 ◽  
Vol 2005 (18) ◽  
pp. 2895-2912 ◽  
Author(s):  
Lucio R. Berrone
Keyword(s):  
Mean Value ◽  
Cauchy Means

The notion of invariance under transformations (changes of coordinates) of the Cauchy mean-value expression is introduced and then used in furnishing a suitable two-variable version of a result by L. Losonczi on equality of many-variable Cauchy means. An assessment of the methods used by Losonczi and Matkowski is made and an alternative way is proposed to solve the problem of representation of two-variable Cauchy means.

scholarly journals Refinements of Results about Weighted Mixed Symmetric Means and Related Cauchy Means

2011 ◽  
Vol 2011 (1) ◽  
pp. 350973
Author(s):  
László Horváth ◽  
KhuramAli Khan ◽  
J Pečarić
Keyword(s):  
Cauchy Means

Generalized Cauchy means

2015 ◽  
Vol 90 (2) ◽  
pp. 307-328 ◽  
Author(s):  
Lucio R. Berrone
Keyword(s):  
Cauchy Means
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