


Paper's Title:
Generalizations of HermiteHadamard's Inequalities for LogConvex Functions
Author(s):
AiJun Li
School of Mathematics and Informatics,
Henan Polytechnic University,
Jiaozuo City, Henan Province,
454010, China.
liaijun72@163.com
Abstract:
In this article, HermiteHadamard's inequalities are extended in terms of the weighted power mean and logconvex function. Several refinements, generalizations and related inequalities are obtained.
Paper's Title:
Improvement of Jensen's Inequality for Superquadratic Functions
Author(s):
S. Abramovich, B. Ivanković, and J. Pečarić
Department of Mathematics,
University of Haifa,
Haifa 31905,
Israel.
abramos@math.haifa.ac.il
Faculty of Transport and
Trafic Engineering,
University of Zagreb,
Vukelićeva 4, 10000,
Croatia
bozidar.ivankovic@zg.tcom.hr
Faculty of Textile,
University of Zagreb,
Prilaz Baruna Filipovića 30, 10000 Zagreb,
Croatia
pecaric@element.hr
Abstract:
Since 1907, the famous Jensen's inequality has been refined in different manners. In our paper, we refine it applying superquadratic functions and separations of domains for convex functions. There are convex functions which are not superquadratic and superquadratic functions which are not convex. For superquadratic functions which are not convex we get inequalities analogue to inequalities satisfied by convex functions. For superquadratic functions which are convex (including many useful functions) we get refinements of Jensen's inequality and its extensions.
Paper's Title:
On Generalization of Hardytype 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 Hardytype 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 an Extension of Hilbert’s Integral Inequality with Some Parameters
Author(s):
Bicheng Yang
Department of
Mathematics, Guangdong Education College, Guangzhou, Guangdong 510303, People’s
Republic of China.
bcyang@pub.guangzhou.gd.cn
URL:
http://www1.gdei.edu.cn/yangbicheng/index.html
Abstract:
In this paper, by introducing some parameters and estimating the weight function, we give an extension of Hilbert’s integral inequality with a best constant factor. As applications, we consider the equivalent form and some particular results.
Paper's Title:
Error estimates for aproximations of the Fourier transform of functions in Lp spaces
Author(s):
A. Aglic Aljinovic and J. Pecaric
Department of Applied Mathematics,
Faculty of Electrical Engineering and Computing,
University Of Zagreb, Unska 3, 10 000 Zagreb,
Croatia
andrea@zpm.fer.hr
Faculty of Textile Technology,
University of Zagreb, Pierottijeva 6, 10000 Zagreb,
Croatia
pecaric@hazu.hr
Abstract:
New inequalities concerning the Fourier transform are given. Estimates of the difference between two Fourier transforms and even bounds to the associated numerical quadrature formulae are provided as well.
Paper's Title:
A Reverse of the Triangle Inequality in Inner Product Spaces and Applications for Polynomials
Author(s):
I. Brnetić, S. S. Dragomir, R. Hoxha and J. Pečarić
Department of Applied Mathematics, Faculty of Electrical
Engineering and Computing,
University of Zagreb, Unska 3, 10 000 Zagreb,
Croatia
andrea@zpm.fer.hr
School of Computer Science & Mathematics, Victoria University
Po Box 14428, Melbourne Vic 8001
Australia
sever.dragomir@vu.edu.au
URL:http://rgmia.vu.edu.au/dragomir
Faculty of Applied Technical Sciences, University of Prishtina,
Mother
Theresa 5, 38 000 Prishtina
Kosova
razimhoxha@yahoo.com
Faculty of Textile Technology, University of Zagreb,
Pierottijeva 6, 10000
Zagreb,
Croatia
pecaric@hazu.hr
Abstract:
A reverse of the triangle inequality in inner product spaces related to the celebrated DiazMetcalf inequality with applications for complex polynomials is given.
Paper's Title:
Weighted Generalization of the Trapezoidal Rule via Fink Identity
Author(s):
S. Kovač, J. Pečarić and A. Vukelić
Faculty of Geotechnical Engineering, University of Zagreb,
Hallerova aleja 7, 42000 Varaždin,
Croatia.
sanja.kovac@gtfvz.hr
Faculty of Textile Technology, University of Zagreb,
Pierottijeva 6, 10000 Zagreb,
Croatia.
pecaric@hazu.hr
Faculty of Food Technology and Biotechnology, Mathematics department, University of Zagreb,
Pierottijeva 6, 10000 Zagreb,
Croatia.
avukelic@pbf.hr
Abstract:
The weighted Fink identity is given and used to obtain generalized weighted trapezoidal formula for ntime differentiable functions. Also, an error estimate is obtained for this formula.
Paper's Title:
Reverses of the CBS Integral Inequality in Hilbert Spaces and Related Results
Author(s):
I. Brnetić, S. S. Dragomir, R. Hoxha and J. Pečarić
Department of Applied Mathematics, Faculty of Electrical
Engineering and Computing,
University of Zagreb, Unska 3, 10 000 Zagreb,
Croatia
andrea@zpm.fer.hr
School of Computer Science & Mathematics, Victoria University
Po Box 14428, Melbourne Vic 8001
Australia
sever.dragomir@vu.edu.au
URL:http://rgmia.vu.edu.au/dragomir
Faculty of Applied Technical Sciences, University of Prishtina,
Mother
Theresa 5, 38 000 Prishtina
Kosova
razimhoxha@yahoo.com
Faculty of Textile Technology, University of Zagreb,
Pierottijeva 6, 10000
Zagreb,
Croatia
pecaric@hazu.hr
Abstract:
There are many known reverses of the CauchyBunyakovskySchwarz (CBS) inequality in the literature. We obtain here a general integral inequality comprising some of those results and also provide other related inequalities. The discrete case, which is of interest in its own turn, is also analysed.
Paper's Title:
Superquadracity, Bohr's Inequality and Deviation from a Mean Value
Author(s):
S. Abramovich, J. Barić, and J. Pečarić
Department of Mathematics, University of Haifa,
Haifa, 31905,
Israel
abramos@math.haifa.ac.il
FESB, University of Split,
Rudera Bošcovića,
B.B., 21000, Split,
Croatia
jbaric@fesb.hr
Faculty of Textile Technology,
University of Zagreb,
Prilaz Baruna Filipovića,
30, 10000 Zagreb,
Croatia.
pecaric@hazu.hr
Abstract:
Extensions of Bohr's inequality via superquadracity are obtained, where instead of the power p=2 which appears in Bohr's inequality we get similar results when we deal with p≥ 2 and with p≤ 2. Also, via superquadracity we extend a bound for deviation from a Mean Value.
Paper's Title:
Some Remarks on a Result of Bougoffa
Author(s):
James A. Oguntuase, LarsErik Persson and Josip E. Pečarič
Department of
Mathematics,University of Agriculture,
P M B 2240, Abeokuta, Nigeria
Department of Mathematics,
Luleå University of Technology,
SE971 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 a Hilberttype Inequality with the Polygamma Function
Author(s):
Bing He and Bicheng Yang
Department of Mathematics, Guangdong Education College,
Guangzhou, 510303,
China.
Department of Mathematics, Guangdong Education College,
Guangzhou, 510303,
China.
Abstract:
By applying the method of weight function and the technique of real analysis, a Hilberttype inequality with a best constant factor is established, where the best constant factor is made of the polygamma function. Furthermore, the inverse form is given.
Paper's Title:
Fejértype Inequalities
Author(s):
Nicuşor Minculete and FlaviaCorina 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, RO200585,
Romania
fcmitroi@yahoo.com
Abstract:
The aim of this paper is to present some new Fejértype results for convex functions. Improvements of Young's inequality (the arithmeticgeometric mean inequality) and other applications to special means are pointed as well.
Paper's Title:
On Reformations of 2Hilbert Spaces
Author(s):
M. Eshaghi Gordji, A. Divandari, M. R. Safi and Y. J. Cho
Department of Mathematics, Semnan
University,
P.O. Box 35195363, Semnan,
Iran
meshaghi@semnan.ac.ir, madjid.eshaghi@gmail.com
Department of Mathematics, Semnan
University,
Iran
Department of Mathematics, Semnan
University,
Iran
safi@semnan.ac.ir, SafiMohammadReza@yahoo.com
Department of Mathematics Education and
the RINS,
Gyeongsang National University
Chinju 660701,
Korea
Abstract:
In this paper, first, we introduce the new concept of (complex) 2Hilbert spaces, that is, we define the concept of 2inner product spaces with a complex valued 2inner product by using the 2norm. Next, we prove some theorems on Schwartz's inequality, the polarization identity, the parallelogram laws and related important properties. Finally, we give some open problems related to 2Hilbert spaces.
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