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Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti, No. 515=17, 2013.

Original scientific paper

On logarithmic convexity for Giaccardi's difference

Josip Pečarić ; Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia
Atiq Ur Rehman ; Abdus Salam School of Mathematical Sciences, GC University,68-B, New Muslim Town, Lahore 54600, Pakistan

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Abstract

In this paper, the Giaccardi’s difference is considered in
some special cases. By utilizing two classes of the convex functions,
the logarithmic convexity of the Giaccardi’s difference is proved.
The positive semi-definiteness of the matrix generated by Giaccardi’s
difference is shown. Related means of Cauchy type are defined
and monotonicity property of these means is proved. The
related mean value theorems of Cauchy type are also given.

Keywords

Convex function; log-convex function; Giaccardi’s inequality; mean value theorems

Hrčak ID:

104400

URI

https://hrcak.srce.hr/104400

Publication date:

27.6.2013.

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