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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:
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:
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:
Bounds for Two Mappings Associated to
the Hermite-Hadamard Inequality
Author(s):
S. S. Dragomir1,2 and I. Gomm1
1Mathematics, School of Engineering & Science,
Victoria University,
PO Box 14428,
Melbourne City, MC 8001,
Australia.
2School of Computational & Applied Mathematics,
University of
the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa.
sever.dragomir@vu.edu.au
ian.gomm@vu.edu.au
URL: http://rgmia.org/dragomir
Abstract:
Some inequalities concerning two mappings associated to the celebrated Hermite-Hadamard integral inequality for convex function with applications for special means are given.
Paper's Title:
Further Bounds for Two Mappings Related
to the Hermite-Hadamard Inequality
Author(s):
S. S. Dragomir1,2 and I. Gomm1
1Mathematics, School of Engineering & Science,
Victoria University,
PO Box 14428,
Melbourne City, MC 8001,
Australia.
2School of Computational & Applied Mathematics,
University of
the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa.
sever.dragomir@vu.edu.au
ian.gomm@vu.edu.au
URL: http://rgmia.org/dragomir
Abstract:
Some new results concerning two mappings associated to the celebrated Hermite-Hadamard integral inequality for twice differentiable functions with applications for special means are given.
Paper's Title:
Some Applications of Fejér's Inequality for Convex Functions (I)
Author(s):
S.S. Dragomir1,2 and I. Gomm1
1Mathematics, School of
Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia.
URL: http://rgmia.org/dragomir
2School of Computational &
Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa.
Abstract:
Some applications of Fejér's inequality for convex functions are explored. Upper and lower bounds for the weighted integral
under various assumptions for f with applications to the trapezoidal quadrature rule are given. Some inequalities for special means are also provided
Paper's Title:
Inequalities for the Area Balance of Functions of Bounded Variation
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:
We introduce the area balance function associated to a Lebesgue
integrable function f:[a,b] →C by
Several sharp bounds for functions of bounded variation are provided. Applications for Lipschitzian and convex functions are also given.
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