Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
Khayyam Journal of Mathematics
2423-4788
6
2
2020
07
01
Differences of operators of generalized Szász type
141
154
EN
Arun
Kajla
Department of mathematics,
Central University of Haryana,
Haryana-123031,
India.
rachitkajla47@gmail.com
Ruchi
Gupta
Department of Mathematics,
Manav Rachna University,
Faridabad-121004, Haryana, India
ruchigupta@mru.edu.in
10.22034/kjm.2020.109811
We derive the approximation of differences of operators. Firstly, we study quantitative estimates for the difference of generalized Szász operators with generalized Szász-Durrmeyer, Szász-Puãltvänea operators, and generalized Szász--Kantorovich operators. Finally, we obtain the quantitative estimate in terms of the weighted modulus of smoothness for these operators.
Positive approximation process,Szasz operators,Pualtvanea operators
http://www.kjm-math.org/article_109811.html
http://www.kjm-math.org/article_109811_063527dcdf3c26b57d02e2a97cd9e179.pdf
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
Khayyam Journal of Mathematics
2423-4788
6
2
2020
07
01
Admissible inertial manifolds for second order in time evolution equations
155
173
EN
Anh
Minh
Le
Department of Mathematical Analysis, Faculty of Natural Sciences, Hongduc University, Thanh Hoa, Vietnam
leanhminh@hdu.edu.vn
10.22034/kjm.2020.109813
We prove the existence of admissible inertial manifolds<br /> for the second order in time evolution equations of the form<br /> $$ ddot{x}+2varepsilon dot{x}+Ax=f(t,x)$$<br /> when $A$ is positive definite and self-adjoint with a discrete spectrum<br /> and the nonlinear term $f$ satisfies the $varphi$-Lipschitz condition, that is,<br /> $|f(t,x)-f(t,y)|leqslantvarphi(t)left |A^{beta}(x-y)right |$<br /> 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.
Admissible inertial manifolds,second order in time evolution equations,admissible function spaces,Lyapunov--Perron method
http://www.kjm-math.org/article_109813.html
http://www.kjm-math.org/article_109813_372333a09954785108dc346740036a94.pdf
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
Khayyam Journal of Mathematics
2423-4788
6
2
2020
07
01
$n$-Absorbing $I$-ideals
174
179
EN
Ismael
Akray
Department of Mathematics, University of Soran, Erbil city, Kurdistan region, Iraq.
ismaeelhmd@yahoo.com
Mediya
Mrakhan
Department of Mathematics, University of Garmian, Kalar city, Kurdistan
region, Iraq.
medya.bawaxan@garmian.edu.krd
10.22034/kjm.2020.109814
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 $a_1 a_2 dots a_{n+1} in P-IP$, then $a_1 a_2 dots a_{i-1} a_{i+1} dots a_{n+1} in P$ 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.
$2$-absorbing ideal,$n$-absorbing ideal,$I$-prime ideal,Prime ideal,$n$-absorbing $I$-ideal
http://www.kjm-math.org/article_109814.html
http://www.kjm-math.org/article_109814_41bf620131018d2506a78fe17acb8a4a.pdf
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
Khayyam Journal of Mathematics
2423-4788
6
2
2020
07
01
Some classes of Probabilistic Inner product spaces and related inequalities
180
192
EN
Panackal
Harikrishnan
http://orcid.org/0000-0001-7173-9951
Department of Mathematics, Manipal institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka, India.
pkharikrishnans@gmail.com
Bernardo
Lafuerza Guillen
Departamento de Estadistica y Matematica Aplicada, Universidad de Almeria, 04120 Almeria, Spain.
blafuerza@gmail.com
10.22034/kjm.2020.109815
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 Cauchy--Schwarz inequality in this general PIP spaces.
Probabilistic normed spaces,$t$-norm,$t$-conorm
http://www.kjm-math.org/article_109815.html
http://www.kjm-math.org/article_109815_64d0951ded0a74c231310779685b3daa.pdf
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
Khayyam Journal of Mathematics
2423-4788
6
2
2020
07
01
On the Arens regularity of a module action and its extensions
193
198
EN
Sedighe
Barootkoob
Department of Mathematics, University of Bojnord, P.O. Box 1339, Bojnord, Iran.
s.barutkub@ub.ac.ir
10.22034/kjm.2020.109816
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.<br /> Finally, some relationships between the topological centers of certain Banach module actions are investigated.
Bilinear map,Banach algebra,module action,Arens regular
http://www.kjm-math.org/article_109816.html
http://www.kjm-math.org/article_109816_130168186224906cc95a0197cf770c0e.pdf
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
Khayyam Journal of Mathematics
2423-4788
6
2
2020
07
01
Distinguishing number (index) and domination number of a graph
199
205
EN
Saeid
Alikhani
0000-0002-1801-203X
Department of Mathematics, Yazd University, 89195-741, Yazd, Iran
alikhani@yazd.ac.ir
Samaneh
Soltani
Department of Mathematics, Yazd University, 89195-741, Yazd, Iran
s.soltani1979@gmail.com
10.22034/kjm.2020.109817
The distinguishing number (index) of a graph $G$ is the least integer $d$<br /> 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.
distinguishing number,Distinguishing index,Domination number
http://www.kjm-math.org/article_109817.html
http://www.kjm-math.org/article_109817_a3bf156522e2b7558c7dc5148bbbdf86.pdf
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
Khayyam Journal of Mathematics
2423-4788
6
2
2020
07
01
Strong rainbow coloring of unicyclic graphs
206
216
EN
Amin
Rostami
Department of Pure Mathematics, Ferdowsi University
of Mashhad, P.O. Box 1159, Mashhad 91775, Iran
ramin6613@gmail.com
Madjid
Mirzavaziri
Department of Pure Mathematics, Ferdowsi University
of Mashhad, P.O. Box 1159, Mashhad 91775, Iran
mirzavaziri@um.ac.ir
Freydoon
Rahbarnia
Department of Applied Mathematics, Ferdowsi
University of Mashhad, P.O. Box
1159, Mashhad 91775, Iran.
rahbarnia@um.ac.ir
10.22034/kjm.2020.109818
A path in an edge-colored graph is called a textit{rainbow path}, if no two edges of the path are colored the same. An edge-colored graph $G$, is textit{rainbow-connected} if any two vertices are connected by a rainbow path. A rainbow-connected 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.
Rainbow connection number,strong rainbow connection number,unicyclic graph
http://www.kjm-math.org/article_109818.html
http://www.kjm-math.org/article_109818_301fa61eefbf5cce342037ce7790283b.pdf
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
Khayyam Journal of Mathematics
2423-4788
6
2
2020
07
01
Stability result of the Bresse system with delay and boundary feedback
217
235
EN
Hocine
Makheloufi
University of Mascara Mustapha Stambouli, Faculty of Exact Sciences,
Department of Mathematics, P.O. Box 305, Mascara 29000, Algeria.
hocine.makheloufi@univ-mascara.dz
Mounir
Bahlil
University of Mascara Mustapha Stambouli, Faculty of Exact Sciences,
Department of Mathematics, P.O. Box 305, Mascara 29000, Algeria.
mounir.bahlil@univ-mascara.dz
Abbes
Benaissa
Laboratory of Analysis and Control of Partial Differential Equations, Djillali Liabes University,
P. O. Box 89, Sidi Bel Abbes 22000, Algeria
benaissa-abbes@yahoo.com
10.22034/kjm.2020.109819
Our interest in this paper is to analyze the asymptotic<br /> behavior of a Bresse system together with three boundary controls,<br /> with delay terms in the first, second, and third equations.<br /> By using the semigroup method, we prove the global well-posedness of<br /> solutions. Assuming the weights of the delay are small, we establish<br /> the exponential decay of energy to the system by using an<br /> appropriate Lyapunov functional.
Bresse system,delay,global solutions,Stability,damping,exponential decay
http://www.kjm-math.org/article_109819.html
http://www.kjm-math.org/article_109819_a6fe24f2fbf18095d111f0f18897fdc8.pdf
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
Khayyam Journal of Mathematics
2423-4788
6
2
2020
07
01
Anderson's theorem for some class of operators
236
242
EN
Mehdi
Naimi
Department of Systems Engineering,
National Polytechnic School of Oran-Maurice Audin (Ex. ENSET of Oran),
BP 1523 Oran-El M'naouar, 31000 Oran, Algeria.
mehdi.naimi@univ-mosta.dz
Mohammed
Benharrat
Department of Systems Engineering,
National Polytechnic School of Oran-Maurice Audin (Ex. ENSET of Oran),
BP 1523 Oran-El M'naouar, 31000 Oran, Algeria.
mohammed.benharrat@gmail.com
10.22034/kjm.2020.109820
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 infinite-dimensional 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.<br />
Numerical Range,essentially numerical range,essentially normal operator,hyponormal operator,quasicompact operator
http://www.kjm-math.org/article_109820.html
http://www.kjm-math.org/article_109820_543970f9d472b56b147308cd0dc9ecaf.pdf
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
Khayyam Journal of Mathematics
2423-4788
6
2
2020
07
01
Radically principal rings
243
249
EN
Mohamed
Aqalmoun
0000-0002-8864-0437
Sidi Mohamed Ben Abdellah University, Higher Normal school, Fez,
maqalmoun@yahoo.fr
Mounir
El
Ouarrachi
Department of Mathematics, Faculty of Sciences and technologies, University Sidi Mohamed Ben Abdallah Fes, Morocco.
m.elouarrachi@gmail.com
10.22034/kjm.2020.109821
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 zero-dimensional radically principal ring. Finally we give a characterization of polynomial ring to be radically principal.
radical,radically principal,polynomial ring
http://www.kjm-math.org/article_109821.html
http://www.kjm-math.org/article_109821_13bebfe55715bbb4a8fec12a006e6f52.pdf
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
Khayyam Journal of Mathematics
2423-4788
6
2
2020
07
01
Embedding topological spaces in a type of generalized topological spaces
250
256
EN
Amin
Talabeigi
0000000152325008
Department of Mathematics,
Payame Noor University, P.O. Box, 19395-3697, Tehran, Iran.
talabeigi.amin@gmail.com
10.22034/kjm.2020.109822
A stack on a nonempty set $X$ is a collection of nonempty subsets of $X$ that is closed under the operation of superset.<br /> 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 $X^*$.<br /> 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.
Generalized topology,generalized extension,one-point generalized extension,strong generalized topology,Stack
http://www.kjm-math.org/article_109822.html
http://www.kjm-math.org/article_109822_48153543d90491ae26ff4e6f0859818e.pdf
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
Khayyam Journal of Mathematics
2423-4788
6
2
2020
07
01
Approximation for the Bernstein operator of max-product kind in symmetric range
257
273
EN
Ecem
Acar
Department of Mathematics, University of Harran, 63100, Anlurfa, Turkey
karakusecem@harran.edu.tr
Done
Karahan
Department of Mathematics, University of Harran, 63100, Anlurfa, Turkey
dkarahan@harran.edu.tr
Sevilay
Kirci Serenbay
Department of Mathematics, University of Harran, 63100, Anlurfa, Turkey.
sevilaykirci@gmail.com
10.22034/kjm.2020.109823
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 max-product 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 shape-preserving properties.
Max-product,degree of approximation,symmetric range,shape-preserving properties
http://www.kjm-math.org/article_109823.html
http://www.kjm-math.org/article_109823_a7fe73d3f8242f905b067eb48196f51c.pdf