#### Rad HAZU, Matematičke znanosti, Vol. 18 (2014), 73-89.

### GENERALIZATIONS AND IMPROVEMENTS OF AN INEQUALITY OF HARDY-LITTLEWOOD-PÓLYA

### Sadia Khalid and Josip Pečarić

Abdus Salam School of Mathematical Sciences, GC University, 68-B, New Muslim Town,
Lahore 54600, Pakistan

*e-mail:* `saadiakhalid176@gmail.com`
Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovića 28a
10000 Zagreb, Croatia

*e-mail:* `pecaric@element.hr`

**Abstract.** Some generalizations of an inequality of
Hardy-Littlewood-Pólya are presented. We discuss the *n*-exponential convexity
and log-convexity of the functions associated with the linear functional
defined by the generalized inequality and also prove the monotonicity
property of the generalized Cauchy means obtained via this functional. Finally,
we give several examples of the families of functions for which the results
can be applied.

**2010 Mathematics Subject Classification.**
26A48, 26A51, 26D15.

**Key words and phrases.** Non-increasing sequence in mean, Wright-convex function,
*n*-exponential and logarithmic convexity, divided difference.

**Full text (PDF)** (free access)

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CrossRef

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*On an inequality of Hardy-Littlewood-Pólya*, Math. Gazette **79** (1995), 383-385.

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