scholarly journals On Carleman's Inequality

2001 ◽  
Vol 253 (2) ◽  
pp. 691-694 ◽  
Author(s):  
Xiaojing Yang
Keyword(s):  
Carleman’S Inequality ◽  
Carleman's Inequality

On strengthened weighted Carleman's inequality

2003 ◽  
Vol 68 (3) ◽  
pp. 481-490 ◽  
Author(s):  
Aleksandra Čižmešija ◽  
Josip Pecarić ◽  
Lars–Erik Persson
Keyword(s):  
Geometric Mean ◽  
Weighted Arithmetic ◽  
Carleman’S Inequality ◽  
Carleman's Inequality

In this paper we prove a new refinement of the weighted arithmetic-geometric mean inequality and apply this result in obtaining a sharpened version of the weighted Carleman's inequality.

Carleman's Inequality

2003 ◽  
Vol 110 (5) ◽  
pp. 424-431 ◽  
Author(s):  
John Duncan ◽  
Colin M. McGregor
Keyword(s):  
Carleman’S Inequality ◽  
Carleman's Inequality

scholarly journals On some convergences to the constant e and improvements of Carleman’s inequality

2015 ◽  
Vol 31 (2) ◽  
pp. 249-254
Author(s):  
CRISTINEL MORTICI ◽  
◽  
HU YUE ◽  
Keyword(s):  
Constant E ◽  
Carleman’S Inequality ◽  
Carleman's Inequality

We present sharp inequalities related to the sequence (1 + 1/n)n and some applications to Kellers’ limit and Carleman’s inequality.

scholarly journals Estimates of (1+x)1/x involved in Carleman’s inequality and Keller’s limit

Filomat ◽  
2015 ◽  
Vol 29 (7) ◽  
pp. 1535-1539 ◽  
Author(s):  
Cristinel Mortici ◽  
X.J. Jang
Keyword(s):  
Simple Proof ◽  
Direct Proof ◽  
Constant E ◽  
Carleman’S Inequality ◽  
Keller’S Limit ◽  
Carleman's Inequality

The aim of this work is to extend the results obtained by Yang Bicheng and L. Debnath in [Some inequalities involving the constant e and an application to Carleman?s inequality, J. Math. Anal. Appl., 223 (1998), 347-353]. We present a simple proof of our new result which can be also used as a direct proof for Yang Bicheng and L. Debnath results. Finally some applications to generalized Keller?s limit and further directions are provided.

scholarly journals Some refinements and generalizations of Carleman's inequality

2004 ◽  
Vol 2004 (41) ◽  
pp. 2171-2180
Author(s):  
Dah-Yan Hwang
Keyword(s):  
Weight Coefficient ◽  
Carleman’S Inequality ◽  
Carleman's Inequality

We give some refinements and generalizations of Carleman's inequality with weaker condition for weight coefficient.

scholarly journals On the Means of Jordan’s Totient Function

2020 ◽  
Vol 46 (6) ◽  
pp. 1753-1765
Author(s):  
Mohammadreza Esfandiari
Keyword(s):  
Asymptotic Formula ◽  
Geometric Mean ◽  
Harmonic Mean ◽  
Alternating Sums ◽  
Important Means ◽  
Carleman’S Inequality ◽  
Carleman's Inequality

Abstract In this paper, we study some important means of Jordan’s totient function, especially, we obtain asymptotic formula for geometric mean and harmonic mean. We also study alternating sums of Jordan’s totient function and Carleman’s inequality for this function.

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