Glasnik Matematicki, Vol. 48, No. 2 (2013), 335356.
3CONVEX FUNCTIONS AND GENERALIZATIONS OF AN INEQUALITY OF HARDYLITTLEWOODPÓLYA
Sadia Khalid, Josip Pečarić and Marjan Praljak
Abdus Salam School of Mathematical Sciences,
GC University, 68B, New Muslim Town, Lahore 54600, Pakistan
email: saadiakhalid176@gmail.com
Abdus Salam School of Mathematical Sciences,
GC University, 68B, New Muslim Town, Lahore 54600, Pakistan
and
Faculty of Textile Technology,
University of Zagreb, Prilaz baruna Filipovića 28a, 10000 Zagreb, Croatia
email: pecaric@element.hr
Abdus Salam School of Mathematical Sciences,
GC University, 68B, New Muslim Town, Lahore 54600, Pakistan
and
Faculty of Food Technology and Biotechnology, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia
email: mpraljak@pbf.hr
Abstract. In this paper, we present some generalizations of an inequality of HardyLittlewoodPólya. We give the nexponential convexity and logconvexity of the functions associated with the linear functionals defined as the nonnegative 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.
2010 Mathematics Subject Classification.
26A24, 26A48, 26A51, 26D15.
Key words and phrases. Nonincreasing sequence in weighted mean, convex function, 3convex function, nexponential and logarithmic
convexity, mean value theorems, divided difference.
Full text (PDF) (access from subscribing institutions only)
DOI: 10.3336/gm.48.2.08
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