2015
1
1
1
124
A Survey on Ostrowski Type Inequalities Related to Pompeiu's Mean Value Theorem
2
2
In this paper we survey some recent results obtained by the author related to Pompeiu's mean value theorem and inequality. Natural applications to Ostrowski type inequalities that play an important role in Numerical Analysis, Approximation Theory, Probability Theory & Statistics, Information Theory and other fields, are given as well.
1

1
35


Silvestru S.
Dragomir
Mathematics, College of Engineering & Science, Victoria University, P.O.
Box 14428, Melbourne City, MC 8001, Australia.
Mathematics, College of Engineering &
Australia
Ostrowski inequality
Pompeiu's mean inequality
integral inequalities
special means
Invariant Means on CHART Groups
2
2
The purpose of this paper is to give a streamlined proof of the existence and uniqueness of a rightinvariant mean on a CHART group. A CHART group is a slight generalisation of a compact topological group. The existence of an invariant mean on a CHART group can be used to prove Furstenberg's fixed point theorem.
1

36
44


Warren B.
Moors
Department of Mathematics, The University of Auckland, Pr ivate Bag 92019,
Auckland, New Zealand.
Department of Mathematics, The University
New Zealand
Topological group
invariant mean
Furstenberg's xed point theorem
Generalizations of Steffensen's Inequality by AbelGontscharoff Polynomial
2
2
In this paper generalizations of Steffensen's inequality using Abel Gontscharoff interpolating polynomial are obtained. Moreover, in a special case generalizations by AbelGontscharoffpolynomial reduce to known weaker conditions for Steffensen's inequality. Furthermore, Ostrowski type inequalities related to obtained generalizations are given.
1

45
61


Josip
Pečarič
Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovica 28a, 10000 Zagreb, Croatia´
Faculty of Textile Technology, University
Croatia


Anamarija
Perušić
Faculty of Civil Engineering, University of Rijeka, Radmile Matejciˇ c 3,´
51000 Rijeka, Croatia
Faculty of Civil Engineering, University
Croatia


Ksenija
Smoljak
Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovica 28a, 10000 Zagreb, Croatia´
Faculty of Textile Technology, University
Croatia
Steffensen's inequality
AbelGontscharoff polynomial
Ostrowski type inequality
n_exponential convexity
HermiteHadamard Type Inequalities for Mappings whose Derivatives are sConvex in the Second Sense via Fractional Integrals
2
2
In this paper we establish HermiteHadamard type inequalities for mappings whose derivatives are s−convex in the second sense and concave.
1

62
70


Erhan
Set
Department of Mathematics, Faculty of Science and Arts, Ordu University,
Ordu, Turkey
Department of Mathematics, Faculty of Science
Turkey


M. Emin
Özdemir
Ataturk University, K.K. Education Faculty, Department of Mathematics,¨
25240, Campus, Erzurum, Turkey
Ataturk University, K.K. Education Faculty,
Turkey


M. Zeki
Sarikaya
Department of Mathematics, Faculty of Science and Arts, Duzce University,¨
Duzce, Turkey¨
Department of Mathematics, Faculty of Science
Turkey


Filiz
Karakoç
Department of Mathematics, Faculty of Science and Arts, Duzce University,¨
Duzce, Turkey¨
Department of Mathematics, Faculty of Science
Turkey
HermiteHadamard type inequality
s−convex function
RiemannLiouville fractional integral
Approximation Numbers of Composition Operators on Weighted Hardy Spaces
2
2
In this paper we find upper and lower bounds for approximation numbers of compact composition operators on the weighted Hardy spaces Hσ under some conditions on the weight function σ:
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71
81


Ajay K.
Sharma
School of Mathematics, Shri Mata Vaishno Devi University, Kakryal, Katra
182320, J& K, India.
School of Mathematics, Shri Mata Vaishno
India


Ambika
Bhat
Ambika Bhat, School of Mathematics, Shri Mata Vaishno Devi University,
Kakryal, Katra182320, J& K, India.
Ambika Bhat, School of Mathematics, Shri
India
Composition operator
weighted Hardy space
approximation number
Star Selection Principles: A Survey
2
2
We review selected results obtained in the last fifteen years on star selection principles in topology, an important subfield of the field of selection principles theory. The results which we discuss concern also uniform structures and, in particular, topological groups and their generalizations.
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82
106


Ljubiša D.R.
Kočinac
University of Niˇs, Faculty of Sciences and Mathematics, 18000 Niˇs, Serbia
University of Niˇs, Faculty of Sciences and
Serbia
Star selection principles
ASSM
selectively (a)
uniform selection principles
Strongly Zeoproduct Preserving Maps on Normed Algebras Induced by a Bounded Linear Functional
2
2
We introduce the notions of strongly zeroproduct (strongly Jordan zeroproduct) preserving maps on normed algebras. These notions are generalization of the concepts of zeroproduct and Jordan zeroproduct preserving maps. Also for a nonzero vector space V and for a nonzero linear functional f on V, we equip V with a multiplication, converting V into an associative algebra, denoted by Vf . We characterize the zeroproduct (Jordan zeroproduct) preserving maps on Vf . Also we characterize the strongly zeroproduct (strongly Jordan zeroproduct) preserving maps on Vf in the case where V is a normed vector space and f is a continuous linear functional on V. Finally, for polynomials in one variable x over Vf , we shall show that each polynomial of precise degree n ≥ 0, with nonzero constant term has precisely nzeros (counted with multiplicity) in Vf . While, polynomials of precise degree n ≥ 2, with zero constant term have infinitely many zeros when dim(V) ≥2. This shows that the algebraic fundamental theorem for polynomial equations over an arbitrary algebra, is not valid in general.
1

107
114


Ali Reza
Khoddami
Department of Pure Mathematics, University of Shahrood, P. O. Box 3619995161
316, Shahrood, Iran.
Department of Pure Mathematics, University
Iran
(Jordan) zeroproduct preserving map
strongly (Jordan) zeroproduct preserving map
Arens product
polynomial equation
Some Integral Inequalities for α, m, (αm)Logarithmically Convex Functions
2
2
In this paper, the authors establish some HermiteHadamard type inequalities by using elementary inequalities for functions whose first derivative absolute values are α, m, (α, m)logarithmically convex
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115
124


Mevlüt
Tunç
Department of Mathematics, Faculty of Science and Arts, Mustafa Kemal
University, Hatay, 31000, Turkey.
Department of Mathematics, Faculty of Science
Turkey


Ebru
Yüksel
Department of Mathematics, Faculty of Science and Arts, Agrı˘ Ibrahim˙
C¸ ec¸en University, Agrı, 04000, Turkey.˘
Department of Mathematics, Faculty of Science
Turkey
α, m
(α,m)logarithmically convex, Hadamard's inequality,Hölder's inequality, power mean inequality, Cauchy's inequality