2021-01-19T15:51:53Z
http://www.kjm-math.org/?_action=export&rf=summon&issue=14813
Khayyam Journal of Mathematics
Khayyam J. Math.
2020
6
2
Differences of operators of generalized Szász type
Arun
Kajla
Ruchi
Gupta
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
2020
07
01
141
154
http://www.kjm-math.org/article_109811_063527dcdf3c26b57d02e2a97cd9e179.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2020
6
2
Admissible inertial manifolds for second order in time evolution equations
Anh
Le
We prove the existence of admissible inertial manifolds for the second order in time evolution equations of the form $$ \ddot{x}+2\varepsilon \dot{x}+Ax=f(t,x)$$ when $A$ is positive definite and self-adjoint with a discrete spectrum and the nonlinear term $f$ satisfies the $\varphi$-Lipschitz condition, that is, $\|f(t,x)-f(t,y)\|\leqslant\varphi(t)\left \|A^{\beta}(x-y)\right \|$ 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.
Admissible inertial manifolds
second order in time evolution equations
admissible function spaces
Lyapunov--Perron method
2020
07
01
155
173
http://www.kjm-math.org/article_109813_372333a09954785108dc346740036a94.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2020
6
2
$n$-Absorbing $I$-ideals
Ismael
Akray
Mediya
Mrakhan
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 $i\in \left\{1,\ 2,\ \dots ,\ {n+1} \right\}$. 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
2020
07
01
174
179
http://www.kjm-math.org/article_109814_41bf620131018d2506a78fe17acb8a4a.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2020
6
2
Some classes of Probabilistic Inner product spaces and related inequalities
Panackal
Harikrishnan
Bernardo
Lafuerza Guillen
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
2020
07
01
180
192
http://www.kjm-math.org/article_109815_64d0951ded0a74c231310779685b3daa.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2020
6
2
On the Arens regularity of a module action and its extensions
Sedighe
Barootkoob
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.
Bilinear map
Banach algebra
module action
Arens regular
2020
07
01
193
198
http://www.kjm-math.org/article_109816_130168186224906cc95a0197cf770c0e.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2020
6
2
Distinguishing number (index) and domination number of a graph
Saeid
Alikhani
Samaneh
Soltani
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.
distinguishing number
Distinguishing index
Domination number
2020
07
01
199
205
http://www.kjm-math.org/article_109817_a3bf156522e2b7558c7dc5148bbbdf86.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2020
6
2
Strong rainbow coloring of unicyclic graphs
Amin
Rostami
Madjid
Mirzavaziri
Freydoon
Rahbarnia
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
2020
07
01
206
216
http://www.kjm-math.org/article_109818_301fa61eefbf5cce342037ce7790283b.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2020
6
2
Stability result of the Bresse system with delay and boundary feedback
Hocine
Makheloufi
Mounir
Bahlil
Abbes
Benaissa
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 well-posedness 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.
Bresse system
delay
global solutions
Stability
damping
exponential decay
2020
07
01
217
235
http://www.kjm-math.org/article_109819_a6fe24f2fbf18095d111f0f18897fdc8.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2020
6
2
Anderson's theorem for some class of operators
Mehdi
Naimi
Mohammed
Benharrat
Anderson's theorem states that if the numerical range of an $n\times n$ 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.
Numerical Range
essentially numerical range
essentially normal operator
hyponormal operator
quasicompact operator
2020
07
01
236
242
http://www.kjm-math.org/article_109820_543970f9d472b56b147308cd0dc9ecaf.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2020
6
2
Radically principal rings
Mohamed
Aqalmoun
Mounir
Ouarrachi
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
2020
07
01
243
249
http://www.kjm-math.org/article_109821_13bebfe55715bbb4a8fec12a006e6f52.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2020
6
2
Embedding topological spaces in a type of generalized topological spaces
Amin
Talabeigi
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.
Generalized topology
generalized extension
one-point generalized extension
strong generalized topology
Stack
2020
07
01
250
256
http://www.kjm-math.org/article_109822_48153543d90491ae26ff4e6f0859818e.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2020
6
2
Approximation for the Bernstein operator of max-product kind in symmetric range
Ecem
Acar
Done
Karahan
Sevilay
Kirci Serenbay
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
2020
07
01
257
273
http://www.kjm-math.org/article_109823_a7fe73d3f8242f905b067eb48196f51c.pdf