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The Australian Journal of Mathematical Analysis and Applications
ISSN 1449-5910 |
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Paper's Title:
Hardy Type Inequalities via Convexity - The Journey so Far
Author(s):
James A.
Oguntuase and Lars-Erik Persson
Department of Mathematics,
University of Agriculture,
P. M. B. 2240, Abeokuta, Nigeria.
Department of
Mathematics, Luleå University of Technology,
SE-971 87, Luleå , Sweden.
oguntuase@yahoo.com,
larserik@sm.luth.se .
Abstract:
It is nowadays well-known that Hardy's inequality (like many other inequalities) follows directly from Jensen's inequality. Most of the development of Hardy type inequalities has not used this simple fact, which obviously was unknown by Hardy himself and many others. Here we report on some results obtained in this way mostly after 2002 by mainly using this fundamental idea.
Paper's Title:
Some Remarks on a Result of Bougoffa
Author(s):
James A. Oguntuase, Lars-Erik Persson and Josip E. Pečarič
Department of
Mathematics,University of Agriculture,
P M B 2240, Abeokuta, Nigeria
Department of Mathematics,
Luleå University of Technology,
SE-971 87, Luleå , Sweden
Faculty of Textile Technology, University of Zagreb,
Pierottijeva 6, 10000 Zagreb, Croatia
oguntuase@yahoo.com,
larserik@sm.luth.se,
pecaric@hazu.hr.
Abstract:
Some new generalizations of the result of
L. Bougoffa [J. Inequal. Pure Appl. Math. 7 (2) (2006), Art. 60]
are derived and discussed.
Paper's Title:
On Generalization of Hardy-type Inequalities
Author(s):
K. Rauf, S. Ponnusamy and J. O. Omolehin
Department of Mathematics,
University of Ilorin, Ilorin,
Nigeria
krauf@unilorin.edu.ng
Department of Mathematics,
Indian Institute of Technology Madras,
Chennai- 600 036,
India
samy@iitm.ac.in
Department of Mathematics,
University of Ilorin, Ilorin,
Nigeria
omolehin_joseph@yahoo.com
Abstract:
This paper is devoted to some new generalization of Hardy-type integral inequalities and the reversed forms. The study is to determine conditions on which the generalized inequalities hold using some known hypothesis. Improvement of some inequalities are also presented.
Paper's Title:
On the Boundedness of Hardy's Averaging Operators
Author(s):
Dah-Chin Luor
Department of Applied Mathematics,
I-Shou University, Dashu District,
Kaohsiung City 84001,
Taiwan, R.O.C.
dclour@isu.edu.tw
Abstract:
In this paper we establish scales of sufficient conditions for the boundedness of Hardy's averaging operators on weighted Lebesgue spaces. The estimations of the operator norms are also obtained. Included in particular are the Erdélyi-Kober operators.
Paper's Title:
Error Inequalities for Weighted Integration Formulae and Applications
Author(s):
Nenad Ujević and Ivan Lekić
Department of Mathematics
University of Split
Teslina 12/III, 21000 Split
CROATIA.
ujevic@pmfst.hr
ivalek@pmfst.hr
Abstract:
Weighted integration formulae are derived. Error inequalities for the
weighted integration formulae are obtained. Applications to some special
functions are also given.
Paper's Title:
Fejér-type Inequalities
Author(s):
Nicuşor Minculete and Flavia-Corina Mitroi
"Dimitrie Cantemir" University,
107 Bisericii Române Street, Braşov, 500068,
România
minculeten@yahoo.com
University of Craiova, Department of Mathematics,
Street A. I. Cuza
13, Craiova, RO-200585,
Romania
fcmitroi@yahoo.com
Abstract:
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.
Paper's Title:
Ostrowski Type Inequalities for Lebesgue Integral: a Survey of Recent Results
Author(s):
Sever S. Dragomir1,2
1Mathematics, School of Engineering
& Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au
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
URL:
http://rgmia.org/dragomir
Abstract:
The main aim of this survey is to present recent results concerning Ostrowski type inequalities for the Lebesgue integral of various classes of complex and real-valued functions. The survey is intended for use by both researchers in various fields of Classical and Modern Analysis and Mathematical Inequalities and their Applications, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.
Paper's Title:
Generalizations of Hermite-Hadamard's Inequalities for Log-Convex Functions
Author(s):
Ai-Jun Li
School of Mathematics and Informatics,
Henan Polytechnic University,
Jiaozuo City, Henan Province,
454010, China.
liaijun72@163.com
Abstract:
In this article, Hermite-Hadamard's inequalities are extended in
terms of the weighted power mean and log-convex
function. Several refinements, generalizations and related
inequalities are obtained.
Paper's Title:
Ostrowski Type Fractional Integral Inequalities for Generalized (s,m,
Author(s):
Artion Kashuri and Rozana Liko
University of Vlora "Ismail Qemali",
Faculty of Technical Science,
Department of Mathematics, 9400,
Albania.
E-mail:
artionkashuri@gmail.com
E-mail: rozanaliko86@gmail.com
Abstract:
In the present paper, the notion of generalized (s,m,φ)-preinvex function is introduced and some new integral inequalities for the left hand side of Gauss-Jacobi type quadrature formula involving generalized (s,m,φ)-preinvex functions along with beta function are given. Moreover, some generalizations of Ostrowski type inequalities for generalized (s,m,φ)-preinvex functions via Riemann-Liouville fractional integrals are established.
Paper's Title:
Inequalities for Discrete F-Divergence Measures: A Survey of Recent Results
Author(s):
Sever S. Dragomir1,2
1Mathematics, School of Engineering
& Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au
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
URL:
http://rgmia.org/dragomir
Abstract:
In this paper we survey some recent results obtained by the author in providing various bounds for the celebrated f-divergence measure for various classes of functions f. Several techniques including inequalities of Jensen and Slater types for convex functions are employed. Bounds in terms of Kullback-Leibler Distance, Hellinger Discrimination and Varation distance are provided. Approximations of the f-divergence measure by the use of the celebrated Ostrowski and Trapezoid inequalities are obtained. More accurate approximation formulae that make use of Taylor's expansion with integral remainder are also surveyed. A comprehensive list of recent papers by several authors related this important concept in information theory is also included as an appendix to the main text.
Paper's Title:
Relation Between The Set Of Non-decreasing Functions And The Set Of Convex Functions
Author(s):
Qefsere Doko Gjonbalaj and Luigj Gjoka
Department of Mathematics, Faculty of
Electrical and Computer Engineering,
University of Prishtina "Hasan Prishtina",
Prishtine 10000,
Kosova
E-mail:
qefsere.gjonbalaj@uni-pr.edu
Department of Engineering Mathematics,
Polytechnic University of Tirana, Tirana,
Albania.
E-mail: luigjgjoka@ymail.com
Abstract:
In this article we address the problem of integral presentation of a convex function. Let I be an interval in R. Here, using the Riemann or Lebesgue’s integration theory, we find the necessary and sufficient condition for a function f: I→ R to be convex in I.
Paper's Title:
Bounds on the Jensen Gap, and Implications for Mean-Concentrated Distributions
Author(s):
Xiang Gao, Meera Sitharam, Adrian E. Roitberg
Department of Chemistry, and Department
of Computer & Information Science & Engineering,
University of Florida,
Gainesville, FL 32611,
USA.
E-mail: qasdfgtyuiop@gmail.com
URL:
https://scholar.google.com/citations?user=t2nOdxQAAAAJ
Abstract:
This paper gives upper and lower bounds on the gap in Jensen's inequality, i.e., the difference between the expected value of a function of a random variable and the value of the function at the expected value of the random variable. The bounds depend only on growth properties of the function and specific moments of the random variable. The bounds are particularly useful for distributions that are concentrated around the mean, a commonly occurring scenario such as the average of i.i.d. samples and in statistical mechanics.
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