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 109811 10.22034/kjm.2020.109811 EN Arun Kajla Department of mathematics, Central University of Haryana, Haryana-123031, India. Ruchi Gupta Department of Mathematics, Manav Rachna University, Faridabad-121004, Haryana, India Journal Article 2019 04 17 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. 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 109813 10.22034/kjm.2020.109813 EN Anh Minh Le Department of Mathematical Analysis, Faculty of Natural Sciences, Hongduc University, Thanh Hoa, Vietnam Journal Article 2019 05 13 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. 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 109814 10.22034/kjm.2020.109814 EN Ismael Akray Department of Mathematics, University of Soran, Erbil city, Kurdistan region, Iraq. Mediya Mrakhan Department of Mathematics, University of Garmian, Kalar city, Kurdistan region, Iraq. Journal Article 2019 04 10 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. 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 109815 10.22034/kjm.2020.109815 EN Panackal Harikrishnan Department of Mathematics, Manipal institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka, India. http://orcid.org/0000-0001-7173-9951 Bernardo Lafuerza Guillen Departamento de Estadistica y Matematica Aplicada, Universidad de Almeria, 04120 Almeria, Spain. Journal Article 2019 10 15 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. 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 109816 10.22034/kjm.2020.109816 EN Sedighe Barootkoob Department of Mathematics, University of Bojnord, P.O. Box 1339, Bojnord, Iran. Journal Article 2019 06 26 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. 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 109817 10.22034/kjm.2020.109817 EN Saeid Alikhani Department of Mathematics, Yazd University, 89195-741, Yazd, Iran 0000-0002-1801-203X Samaneh Soltani Department of Mathematics, Yazd University, 89195-741, Yazd, Iran Journal Article 2019 01 27 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. 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 109818 10.22034/kjm.2020.109818 EN Amin Rostami Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran Madjid Mirzavaziri Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran Freydoon Rahbarnia Department of Applied Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran. Journal Article 2019 06 19 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. 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 109819 10.22034/kjm.2020.109819 EN Hocine Makheloufi University of Mascara Mustapha Stambouli, Faculty of Exact Sciences, Department of Mathematics, P.O. Box 305, Mascara 29000, Algeria. Mounir Bahlil University of Mascara Mustapha Stambouli, Faculty of Exact Sciences, Department of Mathematics, P.O. Box 305, Mascara 29000, Algeria. Abbes Benaissa Laboratory of Analysis and Control of Partial Differential Equations, Djillali Liabes University, P. O. Box 89, Sidi Bel Abbes 22000, Algeria Journal Article 2019 10 04 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. 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 109820 10.22034/kjm.2020.109820 EN Mehdi Naimi Department of Systems Engineering, National Polytechnic School of Oran-Maurice Audin (Ex. ENSET of Oran), BP 1523 Oran-El M&#039;naouar, 31000 Oran, Algeria. Mohammed Benharrat Department of Systems Engineering, National Polytechnic School of Oran-Maurice Audin (Ex. ENSET of Oran), BP 1523 Oran-El M&#039;naouar, 31000 Oran, Algeria. Journal Article 2019 08 10 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 />   http://www.kjm-math.org/article_109820_543970f9d472b56b147308cd0dc9ecaf.pdf