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 Mathematics2423-47886220200701Differences of operators of generalized Szász type14115410981110.22034/kjm.2020.109811ENArunKajlaDepartment of mathematics,
Central University of Haryana,
Haryana-123031,
India.RuchiGuptaDepartment of Mathematics,
Manav Rachna University,
Faridabad-121004, Haryana, IndiaJournal Article20190417We 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.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 Mathematics2423-47886220200701Admissible inertial manifolds for second order in time evolution equations15517310981310.22034/kjm.2020.109813ENAnh MinhLeDepartment of Mathematical Analysis, Faculty of Natural Sciences, Hongduc University, Thanh Hoa, VietnamJournal Article20190513We 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.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 Mathematics2423-47886220200701$n$-Absorbing $I$-ideals17417910981410.22034/kjm.2020.109814ENIsmaelAkrayDepartment of Mathematics, University of Soran, Erbil city, Kurdistan region, Iraq.MediyaMrakhanDepartment of Mathematics, University of Garmian, Kalar city, Kurdistan
region, Iraq.Journal Article20190410Let $R$ 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.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 Mathematics2423-47886220200701Some classes of Probabilistic Inner product spaces and related inequalities18019210981510.22034/kjm.2020.109815ENPanackalHarikrishnanDepartment of Mathematics, Manipal institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka, India.http://orcid.org/0000-0001-7173-9951BernardoLafuerza GuillenDepartamento de Estadistica y Matematica Aplicada, Universidad de Almeria, 04120 Almeria, Spain.Journal Article20191015We 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.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 Mathematics2423-47886220200701On the Arens regularity of a module action and its extensions19319810981610.22034/kjm.2020.109816ENSedigheBarootkoobDepartment of Mathematics, University of Bojnord, P.O. Box 1339, Bojnord, Iran.Journal Article20190626It 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.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 Mathematics2423-47886220200701Distinguishing number (index) and domination number of a graph19920510981710.22034/kjm.2020.109817ENSaeidAlikhaniDepartment of Mathematics, Yazd University, 89195-741, Yazd, Iran0000-0002-1801-203XSamanehSoltaniDepartment of Mathematics, Yazd University, 89195-741, Yazd, IranJournal Article20190127The 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.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 Mathematics2423-47886220200701Strong rainbow coloring of unicyclic graphs20621610981810.22034/kjm.2020.109818ENAminRostamiDepartment of Pure Mathematics, Ferdowsi University
of Mashhad, P.O. Box 1159, Mashhad 91775, IranMadjidMirzavaziriDepartment of Pure Mathematics, Ferdowsi University
of Mashhad, P.O. Box 1159, Mashhad 91775, IranFreydoonRahbarniaDepartment of Applied Mathematics, Ferdowsi
University of Mashhad, P.O. Box
1159, Mashhad 91775, Iran.Journal Article20190619A 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.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 Mathematics2423-47886220200701Stability result of the Bresse system with delay and boundary feedback21723510981910.22034/kjm.2020.109819ENHocineMakheloufiUniversity of Mascara Mustapha Stambouli, Faculty of Exact Sciences,
Department of Mathematics, P.O. Box 305, Mascara 29000, Algeria.MounirBahlilUniversity of Mascara Mustapha Stambouli, Faculty of Exact Sciences,
Department of Mathematics, P.O. Box 305, Mascara 29000, Algeria.AbbesBenaissaLaboratory of Analysis and Control of Partial Differential Equations, Djillali Liabes University,
P. O. Box 89, Sidi Bel Abbes 22000, AlgeriaJournal Article20191004Our 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.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 Mathematics2423-47886220200701Anderson's theorem for some class of operators23624210982010.22034/kjm.2020.109820ENMehdiNaimiDepartment of Systems Engineering,
National Polytechnic School of Oran-Maurice Audin (Ex. ENSET of Oran),
BP 1523 Oran-El M'naouar, 31000 Oran, Algeria.MohammedBenharratDepartment of Systems Engineering,
National Polytechnic School of Oran-Maurice Audin (Ex. ENSET of Oran),
BP 1523 Oran-El M'naouar, 31000 Oran, Algeria.Journal Article20190810Anderson'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 /> 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 Mathematics2423-47886220200701Radically principal rings24324910982110.22034/kjm.2020.109821ENMohamedAqalmounSidi Mohamed Ben Abdellah University, Higher Normal school, Fez,0000-0002-8864-0437Mounir ElOuarrachiDepartment of Mathematics, Faculty of Sciences and technologies, University Sidi Mohamed Ben Abdallah Fes, Morocco.Journal Article20190929Let $A$ 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.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 Mathematics2423-47886220200701Embedding topological spaces in a type of generalized topological spaces25025610982210.22034/kjm.2020.109822ENAminTalabeigiDepartment of Mathematics,
Payame Noor University, P.O. Box, 19395-3697, Tehran, Iran.0000000152325008Journal Article20190628A 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.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 Mathematics2423-47886220200701Approximation for the Bernstein operator of max-product kind in symmetric range25727310982310.22034/kjm.2020.109823ENEcemAcarDepartment of Mathematics, University of Harran, 63100, Anlurfa, TurkeyDoneKarahanDepartment of Mathematics, University of Harran, 63100, Anlurfa, TurkeySevilayKirci SerenbayDepartment of Mathematics, University of Harran, 63100, Anlurfa, Turkey.Journal Article20191120In 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.