A Survey on Ostrowski Type Inequalities Related to Pompeiu's Mean Value Theorem
Silvestru S.
Dragomir
Mathematics, College of Engineering & Science, Victoria University, P.O.
Box 14428, Melbourne City, MC 8001, Australia.
author
text
article
2015
eng
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.
Khayyam Journal of Mathematics
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
2423-4788
1
v.
1
no.
2015
1
35
http://www.kjm-math.org/article_12284_af45b6a7333b951a57b6824037c7f2f1.pdf
dx.doi.org/10.22034/kjm.2015.12284
Invariant Means on CHART Groups
Warren B.
Moors
Department of Mathematics, The University of Auckland, Pr ivate Bag 92019,
Auckland, New Zealand.
author
text
article
2015
eng
The purpose of this paper is to give a stream-lined proof of the existence and uniqueness of a right-invariant 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.
Khayyam Journal of Mathematics
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
2423-4788
1
v.
1
no.
2015
36
44
http://www.kjm-math.org/article_12285_6bc81ee57016ba8697ba66be2d2c5808.pdf
dx.doi.org/10.22034/kjm.2015.12285
Generalizations of Steffensen's Inequality by Abel-Gontscharoff Polynomial
Josip
Pečarič
Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovica 28a, 10000 Zagreb, Croatia´
author
Anamarija
Perušić
Faculty of Civil Engineering, University of Rijeka, Radmile Matejciˇ c 3,´
51000 Rijeka, Croatia
author
Ksenija
Smoljak
Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovica 28a, 10000 Zagreb, Croatia´
author
text
article
2015
eng
In this paper generalizations of Steffensen's inequality using Abel- Gontscharoff interpolating polynomial are obtained. Moreover, in a special case generalizations by Abel-Gontscharoffpolynomial reduce to known weaker conditions for Steffensen's inequality. Furthermore, Ostrowski type inequalities related to obtained generalizations are given.
Khayyam Journal of Mathematics
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
2423-4788
1
v.
1
no.
2015
45
61
http://www.kjm-math.org/article_12286_591d273366dd3ffe68de2b826be60f2e.pdf
dx.doi.org/10.22034/kjm.2015.12286
Hermite-Hadamard Type Inequalities for Mappings whose Derivatives are s-Convex in the Second Sense via Fractional Integrals
Erhan
Set
Department of Mathematics, Faculty of Science and Arts, Ordu University,
Ordu, Turkey
author
M. Emin
Özdemir
Ataturk University, K.K. Education Faculty, Department of Mathematics,¨
25240, Campus, Erzurum, Turkey
author
M. Zeki
Sarikaya
Department of Mathematics, Faculty of Science and Arts, Duzce University,¨
Duzce, Turkey¨
author
Filiz
Karakoç
Department of Mathematics, Faculty of Science and Arts, Duzce University,¨
Duzce, Turkey¨
author
text
article
2015
eng
In this paper we establish Hermite-Hadamard type inequalities for mappings whose derivatives are s−convex in the second sense and concave.
Khayyam Journal of Mathematics
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
2423-4788
1
v.
1
no.
2015
62
70
http://www.kjm-math.org/article_12287_66450089acf1d99d142618724dd09acc.pdf
dx.doi.org/10.22034/kjm.2015.12287
Approximation Numbers of Composition Operators on Weighted Hardy Spaces
Ajay K.
Sharma
School of Mathematics, Shri Mata Vaishno Devi University, Kakryal, Katra-
182320, J& K, India.
author
Ambika
Bhat
Ambika Bhat, School of Mathematics, Shri Mata Vaishno Devi University,
Kakryal, Katra-182320, J& K, India.
author
text
article
2015
eng
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:
Khayyam Journal of Mathematics
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
2423-4788
1
v.
1
no.
2015
71
81
http://www.kjm-math.org/article_12288_4a020ff86c83907640bf945ed0fd20ac.pdf
dx.doi.org/10.22034/kjm.2015.12288
Star Selection Principles: A Survey
Ljubiša D.R.
Kočinac
University of Niˇs, Faculty of Sciences and Mathematics, 18000 Niˇs, Serbia
author
text
article
2015
eng
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.
Khayyam Journal of Mathematics
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
2423-4788
1
v.
1
no.
2015
82
106
http://www.kjm-math.org/article_12289_aaa2b7fd611237872880bdae2d7d649d.pdf
dx.doi.org/10.22034/kjm.2015.12289
Strongly Zeo-product Preserving Maps on Normed Algebras Induced by a Bounded Linear Functional
Ali Reza
Khoddami
Department of Pure Mathematics, University of Shahrood, P. O. Box 3619995161-
316, Shahrood, Iran.
author
text
article
2015
eng
We introduce the notions of strongly zero-product (strongly Jordan zero-product) preserving maps on normed algebras. These notions are generalization of the concepts of zero-product and Jordan zero-product preserving maps. Also for a non-zero vector space V and for a non-zero linear functional f on V, we equip V with a multiplication, converting V into an associative algebra, denoted by Vf . We characterize the zero-product (Jordan zero-product) preserving maps on Vf . Also we characterize the strongly zero-product (strongly Jordan zero-product) 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 non-zero constant term has precisely n-zeros (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.
Khayyam Journal of Mathematics
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
2423-4788
1
v.
1
no.
2015
107
114
http://www.kjm-math.org/article_12290_710c39152e24a4b3dbb3fcee40265094.pdf
dx.doi.org/10.22034/kjm.2015.12290
Some Integral Inequalities for α-, m-, (α-m)-Logarithmically Convex Functions
Mevlüt
Tunç
Department of Mathematics, Faculty of Science and Arts, Mustafa Kemal
University, Hatay, 31000, Turkey.
author
Ebru
Yüksel
Department of Mathematics, Faculty of Science and Arts, Agrı˘ Ibrahim˙
C¸ ec¸en University, Agrı, 04000, Turkey.˘
author
text
article
2015
eng
In this paper, the authors establish some Hermite-Hadamard type inequalities by using elementary inequalities for functions whose first derivative absolute values are α-, m-, (α, m)-logarithmically convex
Khayyam Journal of Mathematics
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
2423-4788
1
v.
1
no.
2015
115
124
http://www.kjm-math.org/article_12291_b2574f963404b7c8037da1340966068e.pdf
dx.doi.org/10.22034/kjm.2015.12291