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:

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.t-com.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 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 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

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 Diaz-Metcalf 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 n-time 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 Cauchy-Bunyakovsky-Schwarz (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, 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 a Hilbert-type Inequality with the Polygamma Function

Author(s):

Bing He and Bicheng Yang
Department of Mathematics, Guangdong Education College,
Guangzhou, 510303,
 China.

hzs314@163.com

Department of Mathematics, Guangdong Education College,
Guangzhou, 510303,
 China.

bcyang@pub.guangzhou.gd.cn

Abstract:

By applying the method of weight function and the technique of real analysis, a Hilbert-type 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:

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:

On Reformations of 2--Hilbert Spaces

Author(s):

M. Eshaghi Gordji, A. Divandari, M. R. Safi and Y. J. Cho

Department of Mathematics, Semnan University,
P.O. Box 35195--363, Semnan,
Iran

meshaghi@semnan.ac.ir, madjid.eshaghi@gmail.com

Department of Mathematics, Semnan University,
Iran

Divandari@sun.Semnan.ac.ir

Department of Mathematics, Semnan University,
Iran

safi@semnan.ac.ir, SafiMohammadReza@yahoo.com

Department of Mathematics Education and the RINS,
Gyeongsang National University
Chinju 660-701,
Korea

yjcho@gnu.ac.kr

Abstract:

In this paper, first, we introduce the new concept of (complex) 2--Hilbert spaces, that is, we define the concept of 2--inner product spaces with a complex valued 2--inner product by using the 2--norm. 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 2--Hilbert spaces.

Paper's Title:

New Refinements for Integral and Sum Forms of Generalized Hölder Inequality For N Term

Author(s):

M. Jakfar, Manuharawati, D. Savitri

Mathematics Department,
Universitas Negeri Surabaya
Jalan Ketintang Gedung C8, Surabaya, 60321
Indonesia.
E-mail: muhammadjakfar@unesa.ac.id
manuharawati@unesa.ac.id
diansavitri@unesa.ac.id

Abstract:

We know that in the field of functional analysis, Hölder inequality is very well known, important, and very applicable. So many researchers are interested in discussing these inequalities. Many world mathematicians try to improve these inequalities. In general, the Hölder inequality has two forms, namely the integral form and the sum form. In this paper, we will introduce a new refinement of the generalization of Hölder inequalities in both integral and addition forms. Especially in the sum form, improvements will be introduced that are better than the previous improvements that have been published by Jing-feng Tian, Ming-hu Ha, and Chao Wang.

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