The Australian Journal of Mathematical Analysis and Applications

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ISSN 1449-5910  


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4: Paper Source PDF document

Paper's Title:

Fejér-type Inequalities


Nicuşor Minculete and Flavia-Corina Mitroi

"Dimitrie Cantemir" University,
107 Bisericii Române Street, Braşov, 500068,

University of Craiova, Department of Mathematics,
Street A. I. Cuza 13, Craiova, RO-200585,


The aim of this paper is to present some new Fejér-type results for convex functions. Improvements of Young's inequality (the arithmetic-geometric mean inequality) and other applications to special means are pointed as well.

2: Paper Source PDF document

Paper's Title:

Hermite-Hadamard Type Inequalities for MN-Convex Functions


Sever S. Dragomir1,2

1Mathematics, College of Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,

2DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa


The present work endeavours to briefly present some of the fundamental results connected to the Hermite-Hadamard inequality for special classes of convex functions such as AG, AH, GA, GG, GH, HA, HG and HH -convex functions in which the author have been involved during the last five years. For simplicity, we call these classes of functions such as MN-convex functions, where M and N stand for any of the Arithmetic (A), Geometric (G) or Harmonic (H) weighted means of positive real numbers. The survey is intended for use by both researchers in various fields of Approximation Theory and Mathematical Inequalities, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.

1: Paper Source PDF document

Paper's Title:

Some New Inequalities of Hermite-Hadamard and Fejér Type for Certain Functions with Higher Convexity


Steven G. From

Department of Mathematics,
University of Nebraska at Omaha,
Omaha, Nebraska 68182-0243,


In this paper, we present some new inequalities of Hermite-Hadamard or Fejér type for certain functions satisfying some higher convexity conditions on one or more derivatives.
An open problem is given also.
Some applications to the logarithmic mean are given.

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