2020
6
2
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133
1

Differences of operators of generalized Szász type
http://www.kjmmath.org/article_109811.html
10.22034/kjm.2020.109811
1
We derive the approximation of differences of operators. Firstly, we study quantitative estimates for the difference of generalized Szász operators with generalized SzászDurrmeyer, SzászPuãltvänea operators, and generalized SzászKantorovich operators. Finally, we obtain the quantitative estimate in terms of the weighted modulus of smoothness for these operators.
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141
154


Arun
Kajla
Department of mathematics,
Central University of Haryana,
Haryana123031,
India.
India
rachitkajla47@gmail.com


Ruchi
Gupta
Department of Mathematics,
Manav Rachna University,
Faridabad121004, Haryana, India
India
ruchigupta@mru.edu.in
Positive approximation process
Szasz operators
Pualtvanea operators
1

Admissible inertial manifolds for second order in time evolution equations
http://www.kjmmath.org/article_109813.html
10.22034/kjm.2020.109813
1
We prove the existence of admissible inertial manifolds for the second order in time evolution equations of the form $$ ddot{x}+2varepsilon dot{x}+Ax=f(t,x)$$ when $A$ is positive definite and selfadjoint with a discrete spectrum and the nonlinear term $f$ satisfies the $varphi$Lipschitz condition, that is, $f(t,x)f(t,y)leqslantvarphi(t)left A^{beta}(xy)right $ for $varphi$ belonging to one of the admissible Banach function spaces containing wide classes of function spaces like $L_{p}$spaces, the Lorentz spaces $L_{p,q}$, and many other function spaces occurring in interpolation theory.
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155
173


Anh
Le
Department of Mathematical Analysis, Faculty of Natural Sciences, Hongduc University, Thanh Hoa, Vietnam
Viet Nam
leanhminh@hdu.edu.vn
Admissible inertial manifolds
second order in time evolution equations
admissible function spaces
LyapunovPerron method
1

$n$Absorbing $I$ideals
http://www.kjmmath.org/article_109814.html
10.22034/kjm.2020.109814
1
Let $R$ be a commutative ring with identity, let $ I $ be a proper ideal of $ R $, and let $ n ge 1 $ be a positive integer. In this paper, we introduce a class of ideals that is closely related to the class of $I$prime ideals. A proper ideal $P$ of $R$ is called an {itshape $n$absorbing $I$ideal} if $a_1, a_2, dots , a_{n+1} in R$ with $a_1 a_2 dots a_{n+1} in PIP$, then $a_1 a_2 dots a_{i1} a_{i+1} dots a_{n+1} in P$ for some $iin left{1, 2, dots , {n+1} right}$. Among many results, we show that every proper ideal of a ring $R$ is an {itshape $n$absorbing $I$ideal} if and only if every quotient of $ R$ is a product of $(n+1)$fields.
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174
179


Ismael
Akray
Department of Mathematics, University of Soran, Erbil city, Kurdistan region, Iraq.
Iraq
ismaeelhmd@yahoo.com


Mediya
Mrakhan
Department of Mathematics, University of Garmian, Kalar city, Kurdistan
region, Iraq.
Iraq
medya.bawaxan@garmian.edu.krd
$2$absorbing ideal
$n$absorbing ideal
$I$prime ideal
Prime ideal
$n$absorbing $I$ideal
1

Some classes of Probabilistic Inner product spaces and related inequalities
http://www.kjmmath.org/article_109815.html
10.22034/kjm.2020.109815
1
We give a new definition for probabilistic inner product spaces, which is sufficiently general to encompass the most important class of probabilistic inner product spaces (briefly, PIP spaces). We have established certain classes of PIP spaces and especially, illustrated that how to construct a real inner product from a Menger PIP space. Finally, we have established the analogous of CauchySchwarz inequality in this general PIP spaces.
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180
192


Panackal
Harikrishnan
Department of Mathematics, Manipal institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka, India.
India
pkharikrishnans@gmail.com


Bernardo
Lafuerza Guillen
Departamento de Estadistica y Matematica Aplicada, Universidad de Almeria, 04120 Almeria, Spain.
Spain
blafuerza@gmail.com
Probabilistic normed spaces
$t$norm
$t$conorm
1

On the Arens regularity of a module action and its extensions
http://www.kjmmath.org/article_109816.html
10.22034/kjm.2020.109816
1
It is known that if the second dual $A^{**}$ of a Banach algebra $A$ is Arens regular, then $A$ is Arens regular itself. However, the converse is not true, in general. Young gave an example of an Arens regular Banach algebra whose second dual is not Arens regular. Later Pym has polished Young's example for presenting more applicable examples. In this paper, we mimic the methods of Young and Pym to present examples of some Arens regular bilinear maps and module actions whose some extensions are not Arens regular. Finally, some relationships between the topological centers of certain Banach module actions are investigated.
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193
198


Sedighe
Barootkoob
Department of Mathematics, University of Bojnord, P.O. Box 1339, Bojnord, Iran.
Iran
s.barutkub@ub.ac.ir
Bilinear map
Banach algebra
module action
Arens regular
1

Distinguishing number (index) and domination number of a graph
http://www.kjmmath.org/article_109817.html
10.22034/kjm.2020.109817
1
The distinguishing number (index) of a graph $G$ is the least integer $d$ such that $G$ has a vertex labeling (edge labeling) with $d$ labels that is preserved only by the trivial automorphism. A set $S$ of vertices in $G$ is a dominating set of $G$ if every vertex of $V(G)setminus S$ is adjacent to some vertex in $S$. The minimum cardinality of a dominating set of $G$ is the domination number of $G$. In this paper, we obtain some upper bounds for the distinguishing number and the distinguishing index of a graph based on its domination number.
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199
205


Saeid
Alikhani
Department of Mathematics, Yazd University, 89195741, Yazd, Iran
Iran
alikhani@yazd.ac.ir


Samaneh
Soltani
Department of Mathematics, Yazd University, 89195741, Yazd, Iran
Iran
s.soltani1979@gmail.com
distinguishing number
Distinguishing index
Domination number
1

Strong rainbow coloring of unicyclic graphs
http://www.kjmmath.org/article_109818.html
10.22034/kjm.2020.109818
1
A path in an edgecolored graph is called a textit{rainbow path}, if no two edges of the path are colored the same. An edgecolored graph $G$, is textit{rainbowconnected} if any two vertices are connected by a rainbow path. A rainbowconnected graph is called strongly rainbow connected if for every two distinct vertices $u$ and $v$ of $V(G)$, there exists a rainbow path $P$ from $u$ to $v$ that in the length of $P$ is equal to $d(u,v)$. The notations {rm rc}$(G)$ and {rm src}$(G)$ are the smallest number of colors that are needed in order to make $G$ rainbow connected and strongly rainbow connected, respectively. In this paper, we find the exact value of {rm rc}$(G)$, where $G$ is a unicyclic graph. Moreover, we determine the upper and lower bounds for {rm src}$(G)$, where $G$ is a unicyclic graph, and we show that these bounds are sharp.
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206
216


Amin
Rostami
Department of Pure Mathematics, Ferdowsi University
of Mashhad, P.O. Box 1159, Mashhad 91775, Iran
Iran
ramin6613@gmail.com


Madjid
Mirzavaziri
Department of Pure Mathematics, Ferdowsi University
of Mashhad, P.O. Box 1159, Mashhad 91775, Iran
Iran
mirzavaziri@um.ac.ir


Freydoon
Rahbarnia
Department of Applied Mathematics, Ferdowsi
University of Mashhad, P.O. Box
1159, Mashhad 91775, Iran.
Iran
rahbarnia@um.ac.ir
Rainbow connection number
strong rainbow connection number
unicyclic graph
1

Stability result of the Bresse system with delay and boundary feedback
http://www.kjmmath.org/article_109819.html
10.22034/kjm.2020.109819
1
Our interest in this paper is to analyze the asymptotic behavior of a Bresse system together with three boundary controls, with delay terms in the first, second, and third equations. By using the semigroup method, we prove the global wellposedness of solutions. Assuming the weights of the delay are small, we establish the exponential decay of energy to the system by using an appropriate Lyapunov functional.
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217
235


Hocine
Makheloufi
University of Mascara Mustapha Stambouli, Faculty of Exact Sciences,
Department of Mathematics, P.O. Box 305, Mascara 29000, Algeria.
Algeria
hocine.makheloufi@univmascara.dz


Mounir
Bahlil
University of Mascara Mustapha Stambouli, Faculty of Exact Sciences,
Department of Mathematics, P.O. Box 305, Mascara 29000, Algeria.
Algeria
mounir.bahlil@univmascara.dz


Abbes
Benaissa
Laboratory of Analysis and Control of Partial Differential Equations, Djillali Liabes University,
P. O. Box 89, Sidi Bel Abbes 22000, Algeria
Algeria
benaissaabbes@yahoo.com
Bresse system
delay
global solutions
Stability
damping
exponential decay
1

Anderson's theorem for some class of operators
http://www.kjmmath.org/article_109820.html
10.22034/kjm.2020.109820
1
Anderson's theorem states that if the numerical range of an $ntimes n$ matrix is contained in the closed unit disk and intersects with the unit circle at more than $n$ points, then the numerical range coincides with the closed unit disk. In an infinitedimensional setting, an analogue of this result for a compact operator was established by Gau and Wu and for operator being the sum of a normal and compact operator by Birbonshi et al. We consider here three classes of operators: Operators being the sum of compact and operator with numerical radius strictly less than 1, operators with essentially numerical range coinciding with the convex hull of its essential spectrum, and quasicompact operators.
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236
242


Mehdi
Naimi
Department of Systems Engineering,
National Polytechnic School of OranMaurice Audin (Ex. ENSET of Oran),
BP 1523 OranEl M'naouar, 31000 Oran, Algeria.
Algeria
mehdi.naimi@univmosta.dz


Mohammed
Benharrat
Department of Systems Engineering,
National Polytechnic School of OranMaurice Audin (Ex. ENSET of Oran),
BP 1523 OranEl M'naouar, 31000 Oran, Algeria.
Algeria
mohammed.benharrat@gmail.com
Numerical Range
essentially numerical range
essentially normal operator
hyponormal operator
quasicompact operator
1

Radically principal rings
http://www.kjmmath.org/article_109821.html
10.22034/kjm.2020.109821
1
Let $A$ be a commutative ring. An ideal $I$ of $A$ is radically principal if there exists a principal ideal $J$ of $A$ such that $sqrt{I}=sqrt{J}$. The ring $A$ is radically principal if every ideal of $A$ is radically principal. In this article, we study radically principal rings. We prove an analogue of the Cohen theorem, precisely, a ring is radically principal if and only if every prime ideal is radically principal. Also we characterize a zerodimensional radically principal ring. Finally we give a characterization of polynomial ring to be radically principal.
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243
249


Mohamed
Aqalmoun
Sidi Mohamed Ben Abdellah University, Higher Normal school, Fez,
Morocco
maqalmoun@yahoo.fr


Mounir
Ouarrachi
Department of Mathematics, Faculty of Sciences and technologies, University Sidi Mohamed Ben Abdallah Fes, Morocco.
Morocco
m.elouarrachi@gmail.com
radical
radically principal
polynomial ring
1

Embedding topological spaces in a type of generalized topological spaces
http://www.kjmmath.org/article_109822.html
10.22034/kjm.2020.109822
1
A stack on a nonempty set $X$ is a collection of nonempty subsets of $X$ that is closed under the operation of superset. Let $(X, tau)$ be an arbitrary topological space with a stack $mathcal{S}$, and let $X^*=X cup {p}$ for $p notin X$. In the present paper, using the stack $mathcal{S}$ and the topological closure operator associated to the space $(X, tau)$, we define an envelope operator on $X^*$ to construct a generalized topology $mu_mathcal{S}$ on $X^*$. We then show that the space $(X^*, mu_mathcal{S})$ is the generalized extension of the space $(X, tau)$. We also provide conditions under which $(X^*, mu_mathcal{S})$ becomes a generalized Hausdorff space.
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250
256


Amin
Talabeigi
Department of Mathematics,
Payame Noor University, P.O. Box, 193953697, Tehran, Iran.
Iran
talabeigi.amin@gmail.com
Generalized topology
generalized extension
onepoint generalized extension
strong generalized topology
Stack
1

Approximation for the Bernstein operator of maxproduct kind in symmetric range
http://www.kjmmath.org/article_109823.html
10.22034/kjm.2020.109823
1
In the approximation theory, polynomials are particularly positive linear operators. Nonlinear positive operators by means of maximum and product were introduced by B. Bede. In this paper, the maxproduct of Bernstein operators for symmetric ranges are introduced and some upper estimates of approximation error for some subclasses of functions are obtained. Also, we investigate the shapepreserving properties.
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257
273


Ecem
Acar
Department of Mathematics, University of Harran, 63100, Anlurfa, Turkey
Turkey
karakusecem@harran.edu.tr


Done
Karahan
Department of Mathematics, University of Harran, 63100, Anlurfa, Turkey
Turkey
dkarahan@harran.edu.tr


Sevilay
Kirci Serenbay
Department of Mathematics, University of Harran, 63100, Anlurfa, Turkey.
Turkey
sevilaykirci@gmail.com
Maxproduct
degree of approximation
symmetric range
shapepreserving properties