Original scientific paper

https://doi.org/10.3336/gm.48.2.08

3-convex functions and generalizations of an inequality of Hardy-Littlewood-Pólya

Sadia Khalid orcid.org/0000-0002-9603-3506 ; Abdus Salam School of Mathematical Sciences, GC University, 68-B, New Muslim Town, Lahore 54600, Pakistan
Josip Pečarić ; Abdus Salam School of Mathematical Sciences, GC University, 68-B, New Muslim Town, Lahore 54600, Pakistan and Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovića 28a, 10000 Zagreb, Croatia
Marjan Praljak ; Abdus Salam School of Mathematical Sciences, GC University, 68-B, New Muslim Town, Lahore 54600, Pakistan and Faculty of Food Technology and Biotechnology, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia

Abstract

In this paper, we present some generalizations of an inequality of Hardy-Littlewood-Pólya. We give the n-exponential convexity and log-convexity of the functions associated with the linear functionals defined as the non-negative differences of the generalized inequalities and prove the monotonicity property of the generalized Cauchy means obtained via these functionals. Finally, we give several examples of the families of functions for which the results can be applied.

Keywords

Non-increasing sequence in weighted mean; convex function; 3-convex function; n-exponential and logarithmic convexity; mean value theorems; divided difference

Hrčak ID:

112212

URI

https://hrcak.srce.hr/112212

Publication date:

16.12.2013.

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