]>
2012
5
5
ISSN 2008-1898
104
Necessary and sucient conditions for symmetric homogeneous polynomial inequalities of degree four and six in real variables
Necessary and sucient conditions for symmetric homogeneous polynomial inequalities of degree four and six in real variables
en
en
Let \(f_n(x; y; z)\) be a symmetric homogeneous polynomial of degree \(n = 4\) or \(n = 6\), in three real variables. We
give necessary and sufficient conditions to have \(f_n(x; y; z) \geq 0\) for all real numbers \(x; y; z\). Then, we apply
the obtained results to prove several relevant symmetric homogeneous polynomial inequalities of degree four
and six.
307
320
Vasile
Cirtoaje
Department of Automatic Control and Computers
University of Ploiesti
Romania
vcirtoaje@upg-ploiesti.ro
Symmetric homogeneous polynomial
necessary and sufficient conditions
real variables.
Article.1.pdf
[
[1]
T. Ando, Some Homogeneous Cyclic Inequalities of Three Variables of Degree Three and Four, Aust. J. Math. Anal. Appl., 7 (2010), 1-14
##[2]
V. Cirtoaje, On the Cyclic Homogeneous Polynomial Inequalities of Degree Four, Journal of Inequalities in Pure and Applied Mathematics, 10 (2009), 1-10
##[3]
V. Cirtoaje, Algebraic Inequalities , GIL Publishing House, (2006)
##[4]
, Art of Problem Solving Forum, May, (2009), -
##[5]
, Art of Problem Solving Forum, August, (2009), -
##[6]
, Art of Problem Solving Forum, August, (2010), -
##[7]
, Art of Problem Solving Forum, July, (2009), -
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, Art of Problem Solving Forum, April, (2008), -
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, Art of Problem Solving Forum, March, (2008), -
##[10]
, Art of Problem Solving Forum, May, (2009), -
##[11]
, Art of Problem Solving Forum, February, (2008), -
]
Existence Results for a Second Order Impulsive Neutral Functional Integrodierential Inclusions in Banach Spaces with Innite Delay
Existence Results for a Second Order Impulsive Neutral Functional Integrodierential Inclusions in Banach Spaces with Innite Delay
en
en
A fixed point theorem for condensing maps due to Martelli combined with theories of a strongly continuous cosine
family of bounded linear operators is used to investigate the existence of solutions to second order impulsive neutral
functional integrodifferential inclusions with infinite delay in Banach spaces.
321
333
V.
Kavitha
Department of Mathematics
Karunya University
India
kavi_velubagyam@yahoo.co.in
M. Mallika
Arjunan
Department of Mathematics
Karunya University
India
arjunphd07@yahoo.co.in
C.
Ravichandran
Department of Mathematics
Karunya University
India
ravibirthday@gmail.com
Second order impulsive integrodifferential inclusion
cosine functions of operators
mild solution
Martelli's fixed point theorem.
Article.2.pdf
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]
\(H(.,.)-\eta\)-cocoercive operators and variational-like inclusions in Banach spaces
\(H(.,.)-\eta\)-cocoercive operators and variational-like inclusions in Banach spaces
en
en
In this paper, we define \(H(.,.)-\eta\)-cocoercive operators in q-uniformly smooth Banach spaces and its resolvent
operator. We prove the Lipschitz continuity of the resolvent operator associated with \(H(.,.)-\eta\)-cocoercive
operator and estimate its Lipschitz constant. By using the techniques of resolvent operator, an iterative
algorithm for solving a variational-like inclusion problem is constructed. The existence of solution for the
variational-like inclusions and the convergence of iterative sequences generated by the algorithm is proved.
Some examples are given.
334
344
Rais
Ahmad
Department of Mathematics
Aligarh Muslim University
India
raisain_123@rediffmail.com
Mohammad
Dilshad
Department of Mathematics
Aligarh Muslim University
India
mdilshaad@gmail.com
\(H(.
.)-\eta\)-cocoercive
Algorithm
Inclusion
Banach spaces
Lipschitz continuity.
Article.3.pdf
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[1]
R. Ahmad, M. Dilshad, M. M. Wong, J. C. Yao, H(.,.)-cocoercive operator and an application for solving generalized variational inclusions, Abs. Appl. Anal. Vol. 2011, Article ID 261534, 12 pages (2011)
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]
Sequentially injective and complete acts over a semigroup
Sequentially injective and complete acts over a semigroup
en
en
In this paper using the notion of a sequentially dense monomorphism we consider sequential injectivity
(s-injectivity) for acts over a semigroup S. We show that s-injectivity, s-absolutely retract, and sequential
compactness are equivalent.
345
349
G.
Moghaddasi
Department of Mathematics
Hakim Sabzevary University
Iran
moghaddasimath@yahoo.com
sequential injective
completeness
absolute retract.
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Jensen type inequalities for twice dierentiable functions
Jensen type inequalities for twice dierentiable functions
en
en
In this paper, we give some Jensen-type inequalities for \(\varphi: I\rightarrow\mathbb{R}, I=[\alpha,\beta ]\subset\mathbb{R}\) where \(\varphi\) is a continuous
function on \(I\); twice differentiable on
\(I^°=(\alpha,\beta )\) and there exists \(m = \inf
_{x\in I^°} \varphi ''(x)\) or \(M = \sup_{x\in I^°}\varphi '' (x)\).
Furthermore, if \(\varphi ''\) is bounded on \(I^°\)
; then we give an estimate, from below and from above of Jensen
inequalities.
350
356
Abdallah
El Frissi
Department of Mathematics, Laboratory of Pure and Applied Mathematics
University of Mostaganem (UMAB)
Algeria
elfarissi.abdallah@yahoo.fr
Benharrat
Belaïdi
Department of Mathematics, Laboratory of Pure and Applied Mathematics
University of Mostaganem (UMAB)
Algeria
belaidi@univ-mosta.dz
Zinelaâbidine
Lareuch
Department of Mathematics, Laboratory of Pure and Applied Mathematics
University of Mostaganem (UMAB)
Algeria
z.latreuch@gmail.com
Jensen inequality
Convex functions
Twice differentiable functions
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]
On fuzzy order relations
On fuzzy order relations
en
en
In this review article we present results regarding the fuzzy order relations.The concept of fuzzy order was
introduced by generalizing the notion of reflexivity, antisymmetric and transitivity.
357
378
Ismat
Beg
Lahore University of Management Sciences & University of Central Punjab
Pakistan
ibeg@lums.edu.pk
Ordered set
fuzzy ordered set
Zorn's lemma
fixed point
selection
extension
variational principle
multivalued mapping
fuzzy metric spaces
fuzzy Riesz spaces
fuzzy positive linear operator
Hahn-Banach theorem.
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Uniformly normal structure and uniformly generalized Lipschitzian semigroups
Uniformly normal structure and uniformly generalized Lipschitzian semigroups
en
en
In this work, we introduce some condition on one-parameter semigroup of self-mappings it is called \(k\)-uniformly
generalized Lipschitzian. The condition is weaker than Lipschitzian type conditions. Also, we
show that a \(k\)-generalized Lipschitzian semigroup of nonlinear self-mappings of a nonempty closed convex
subset \(C\) of real Banach space \(X\) admits a common fixed point if the semigroup has a bounded orbit and if
\(k > 0\). Our results extending the results due to L.C. Ceng, H. K. Xu and J.C. Yao [5]
379
388
Ahmed H.
Soliman
Department of Mathematics, Faculty of Science
Al-Azhar University
Egypt
ahsolimanm@gmail.com
Mohamed A.
Barakat
Department of Mathematics, Faculty of Science
Al-Azhar University
Egypt
barakat96@yahoo.com
Uniformly normal structure
Uniformly generalized semigroup
Fixed point
Characteristic of convexity
Modulus of convexity.
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]
On convergence theorems for total asymptotically nonexpansive nonself-mappings in Banach spaces
On convergence theorems for total asymptotically nonexpansive nonself-mappings in Banach spaces
en
en
In this paper, we define and study new strong convergence theorems of the modified Mann and the modified
Ishikawa iterative scheme with errors for nonself-mappings which are total asymptotically nonexpansive in
a uniformly convex Banach space.
389
402
Esra
Yolacan
Department of Mathematics, Faculty of Science
Ataturk University
Turkey
yolacanesra@gmail.com
Hukmi
Kiziltunc
Department of Mathematics, Faculty of Science
Ataturk University
Turkey
hukmu@atauni.edu.tr
Asymptotically nonexpansive nonself-mappings
total asymptotically nonexpansive nonself-mappings
common fixed point
uniformly convex Banach space.
Article.8.pdf
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Ya. I. Albert, C. E. Chidume, H. Zegeye, Approximating fixed points of total asymptotically nonexpansive mappings, Fixed Point Theory Appl., article ID 10673. (2006)
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]
Weak and strong convergence of an explicit iteration process for an asymptotically quasi-i-nonexpansive mapping in Banach spaces
Weak and strong convergence of an explicit iteration process for an asymptotically quasi-i-nonexpansive mapping in Banach spaces
en
en
In this paper, we prove the weak and strong convergence of an explicit iterative process to a common
fixed point of an asymptotically quasi-I-nonexpansive mapping T and an asymptotically quasi-nonexpansive
mapping I, defined on a nonempty closed convex subset of a Banach space.
403
411
Yunus
Purtas
Banking and Insurance Department, Ahmetli Vocational Higher School
Celal Bayar University
Turkey
yunus.purtas@cbu.edu.tr
Hukmi
Kiziltunc
Department of Mathematics, Faculty of Science
Ataturk University
Turkey
hukmu@atauni.edu.tr
Asymptotically quasi-I-nonexpansive self-mappings
explicit iterations
common fixed point
uniformly convex Banach space.
Article.9.pdf
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]