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The Australian Journal of Mathematical Analysis and Applications
ISSN 1449-5910 |
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Paper's Title:
A Wallis Type Inequality and a Double Inequality for Probability Integral
Author(s):
Jian Cao, Da-Wei Niu and Feng Qi
School of Mathematics and Informatics,
Henan Polytechnic University, Jiaozuo City,
Henan Province, 454010,
China
21caojian@163.com
School of Mathematics and Informatics,
Henan Polytechnic University, Jiaozuo City,
Henan Province, 454010,
China
nnddww@tom.com
Research Institute of Mathematical Inequality Theory,
Henan Polytechnic University, Jiaozuo City,
Henan Province, 454010,
China
qifeng@hpu.edu.cn
fengqi618@member.ams.org
qifeng618@hotmail.com
qifeng618@msn.com
qifeng618@qq.com
URL: http://rgmia.vu.edu.au/qi.html
Abstract:
In this short note, a Wallis type inequality with the best upper and lower
bounds is established. As an application, a double inequality for the
probability integral is found.
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:
Some New Inequalities of Hermite-Hadamard and Fejér Type for Certain Functions with Higher Convexity
Author(s):
Steven G. From
Department of Mathematics,
University of Nebraska at Omaha,
Omaha, Nebraska 68182-0243,
U.S.A.
E-mail: sfrom@unomaha.edu
Abstract:
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.
Paper's Title:
Monotonicity Properties for Generalized Logarithmic Means
Author(s):
Chao-Ping Chen and Feng Qi
Department of Applied Mathematics and Informatics,
Research Institute of Applied Mathematics,
Henan Polytechnic University, Jiaozuo
City, Henan 454000, China
chenchaoping@hpu.edu.cn
Department of Applied Mathematics and Informatics,
Research Institute of Applied Mathematics,
Henan Polytechnic University, Jiaozuo
City, Henan 454000, China
qifeng@hpu.edu.cn,
fengqi618@member.ams.org
Url:
http://rgmia.vu.edu.au/qi.html,
http://dami.hpu.edu.cn/qifeng.html
Abstract:
In this paper, we consider the monotonicity properties for ratio of two generalized logarithmic means, and then use it to extend and complement a recently published result of F. Qi and B.-N. Guo.
Paper's Title:
Residual-Based A Posteriori Error Estimates For A Conforming Mixed Finite Element Discretization of the Monge-Ampere Equation
Author(s):
J. Adetola, K. W. Houedanou and B. Ahounou
Institut de Mathematiques et de Sciences
Physiques (IMSP),
Universite d'Abomey-Calavi
E-mail: adetolajamal58@yahoo.com
Departement de Mathematiques,
Faculte des Sciences et Techniques (FAST),
Universite d'Abomey-Calavi
E-mail: khouedanou@yahoo.fr
Departement de Mathematiques,
Faculte des Sciences et Techniques (FAST),
Universite d'Abomey-Calavi
E-mail: bahounou@yahoo.fr
Abstract:
In this paper we develop a new a posteriori error analysis for the Monge-Ampere equation approximated by conforming finite element method on isotropic meshes in R2. The approach utilizes a slight variant of the mixed discretization proposed by Gerard Awanou and Hengguang Li in [4]. The a posteriori error estimate is based on a suitable evaluation on the residual of the finite element solution. It is proven that the a posteriori error estimate provided in this paper is both reliable and efficient.
Paper's Title:
New Reverses of Schwarz, Triangle and Bessel Inequalities in Inner Product Spaces
Author(s):
S. S. Dragomir
School of Computer Science and Mathematics, Victoria
University of Technology, PO BOX
14428, MCMC 8001, VICTORIA, AUSTRALIA.
sever.dragomir@vu.edu.au
URL:
http://rgmia.vu.edu.au/SSDragomirWeb.html
Abstract:
New reverses of the Schwarz, triangle and Bessel inequalities in inner product spaces are pointed out. These results complement the recent ones obtained by the author in the earlier paper [13]. Further, they are employed to establish new Grüss type inequalities. Finally, some natural integral inequalities are stated as well.
Paper's Title:
Quantitative Estimates for Positive Linear Operators Obtained by Means of Piecewise Linear Functions
Author(s):
Vasile Mihesan
Technical University of Cluj-Napoca,
Department of Mathematics,
Str. C. Daicoviciu 15,
Cluj-Napoca,
Romania
Vasile.Mihesan@math.utcluj.ro
Abstract:
In this paper we obtain estimates for the remainder in approximating continuous
functions by positive linear operators, using piecewise linear functions.
Paper's Title:
Applications of Relations and Relators in the
Extensions of Stability Theorems for Homogeneous and Additive Functions
Author(s):
Árpád Száz
Institute of Mathematics, University of Debrecen,
H-4010 Debrecen,
Pf. 12,
Hungary
szaz@math.klte.hu
Abstract:
By working out an appropriate technique of relations and relators and extending the ideas of the direct methods of Z. Gajda and R. Ger, we prove some generalizations of the stability theorems of D. H. Hyers, T. Aoki, Th. M. Rassias and P. Găvruţă in terms of the existence and unicity of 2-homogeneous and additive approximate selections of generalized subadditive relations of semigroups to vector relator spaces. Thus, we obtain generalizations not only of the selection theorems of Z. Gajda and R. Ger, but also those of the present author.
Paper's Title:
Weyl's theorem for class Q and k - quasi class Q Operators
Author(s):
S. Parvatham and D. Senthilkumar
Department of Mathematics and Humanities,
Sri Ramakrishna Institute of Technology, Coimbatore-10, Tamilnadu,
India.
E-mail: parvathasathish@gmail.com
Post Graduate and Research Department of
Mathematics,
Govt. Arts College, Coimbatore-641018, Tamilnadu,
India.
E-mail: senthilsenkumhari@gmail.com
Abstract:
In this paper, we give some properties of class Q operators. It is proved that every class Q operators satisfies Weyl's theorem under the condition that T2 is isometry. Also we proved that every k quasi class Q operators is Polaroid and the spectral mapping theorem holds for this class of operator. It will be proved that single valued extension property, Weyl and generalized Weyl's theorem holds for every k quasi class Q operators.
Paper's Title:
Trace Inequalities for Operators in Hilbert Spaces: 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:
https://rgmia.org/dragomir
Abstract:
In this paper we survey some recent trace inequalities for operators in Hilbert spaces that are connected to Schwarz's, Buzano's and Kato's inequalities and the reverses of Schwarz inequality known in the literature as Cassels' inequality and Shisha-Mond's inequality. Applications for some functionals that are naturally associated to some of these inequalities and for functions of operators defined by power series are given. Further, various trace inequalities for convex functions are presented including refinements of Jensen inequality and several reverses of Jensen's inequality. Hermite-Hadamard type inequalities and the trace version of Slater's inequality are given. Some Lipschitz type inequalities are also surveyed. Examples for fundamental functions such as the power, logarithmic, resolvent and exponential functions are provided as well.
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