Differences of operators of generalized Szász type Arun Kajla Department of mathematics, Central University of Haryana, Haryana-123031, India. author Ruchi Gupta Department of Mathematics, Manav Rachna University, Faridabad-121004, Haryana, India author text article 2020 eng 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. Khayyam Journal of Mathematics 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) 2423-4788 6 v. 2 no. 2020 141 154 http://www.kjm-math.org/article_109811_063527dcdf3c26b57d02e2a97cd9e179.pdf dx.doi.org/10.22034/kjm.2020.109811 Admissible inertial manifolds for second order in time evolution equations Anh Le Department of Mathematical Analysis, Faculty of Natural Sciences, Hongduc University, Thanh Hoa, Vietnam author text article 2020 eng 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. Khayyam Journal of Mathematics 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) 2423-4788 6 v. 2 no. 2020 155 173 http://www.kjm-math.org/article_109813_372333a09954785108dc346740036a94.pdf dx.doi.org/10.22034/kjm.2020.109813 $n$-Absorbing $I$-ideals Ismael Akray Department of Mathematics, University of Soran, Erbil city, Kurdistan region, Iraq. author Mediya Mrakhan Department of Mathematics, University of Garmian, Kalar city, Kurdistan region, Iraq. author text article 2020 eng 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. Khayyam Journal of Mathematics 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) 2423-4788 6 v. 2 no. 2020 174 179 http://www.kjm-math.org/article_109814_41bf620131018d2506a78fe17acb8a4a.pdf dx.doi.org/10.22034/kjm.2020.109814 Some classes of Probabilistic Inner product spaces and related inequalities Panackal Harikrishnan Department of Mathematics, Manipal institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka, India. author Bernardo Lafuerza Guillen Departamento de Estadistica y Matematica Aplicada, Universidad de Almeria, 04120 Almeria, Spain. author text article 2020 eng 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. Khayyam Journal of Mathematics 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) 2423-4788 6 v. 2 no. 2020 180 192 http://www.kjm-math.org/article_109815_64d0951ded0a74c231310779685b3daa.pdf dx.doi.org/10.22034/kjm.2020.109815 On the Arens regularity of a module action and its extensions Sedighe Barootkoob Department of Mathematics, University of Bojnord, P.O. Box 1339, Bojnord, Iran. author text article 2020 eng 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. Khayyam Journal of Mathematics 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) 2423-4788 6 v. 2 no. 2020 193 198 http://www.kjm-math.org/article_109816_130168186224906cc95a0197cf770c0e.pdf dx.doi.org/10.22034/kjm.2020.109816 Distinguishing number (index) and domination number of a graph Saeid Alikhani Department of Mathematics, Yazd University, 89195-741, Yazd, Iran author Samaneh Soltani Department of Mathematics, Yazd University, 89195-741, Yazd, Iran author text article 2020 eng 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. Khayyam Journal of Mathematics 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) 2423-4788 6 v. 2 no. 2020 199 205 http://www.kjm-math.org/article_109817_a3bf156522e2b7558c7dc5148bbbdf86.pdf dx.doi.org/10.22034/kjm.2020.109817 Strong rainbow coloring of unicyclic graphs Amin Rostami Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran author Madjid Mirzavaziri Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran author Freydoon Rahbarnia Department of Applied Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran. author text article 2020 eng 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. Khayyam Journal of Mathematics 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) 2423-4788 6 v. 2 no. 2020 206 216 http://www.kjm-math.org/article_109818_301fa61eefbf5cce342037ce7790283b.pdf dx.doi.org/10.22034/kjm.2020.109818 Stability result of the Bresse system with delay and boundary feedback Hocine Makheloufi University of Mascara Mustapha Stambouli, Faculty of Exact Sciences, Department of Mathematics, P.O. Box 305, Mascara 29000, Algeria. author Mounir Bahlil University of Mascara Mustapha Stambouli, Faculty of Exact Sciences, Department of Mathematics, P.O. Box 305, Mascara 29000, Algeria. author Abbes Benaissa Laboratory of Analysis and Control of Partial Differential Equations, Djillali Liabes University, P. O. Box 89, Sidi Bel Abbes 22000, Algeria author text article 2020 eng 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. Khayyam Journal of Mathematics 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) 2423-4788 6 v. 2 no. 2020 217 235 http://www.kjm-math.org/article_109819_a6fe24f2fbf18095d111f0f18897fdc8.pdf dx.doi.org/10.22034/kjm.2020.109819 Anderson's theorem for some class of operators 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. author 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. author text article 2020 eng 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.   Khayyam Journal of Mathematics 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) 2423-4788 6 v. 2 no. 2020 236 242 http://www.kjm-math.org/article_109820_543970f9d472b56b147308cd0dc9ecaf.pdf dx.doi.org/10.22034/kjm.2020.109820 Radically principal rings Mohamed Aqalmoun Sidi Mohamed Ben Abdellah University, Higher Normal school, Fez, author Mounir Ouarrachi Department of Mathematics, Faculty of Sciences and technologies, University Sidi Mohamed Ben Abdallah Fes, Morocco. author text article 2020 eng 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. Khayyam Journal of Mathematics 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) 2423-4788 6 v. 2 no. 2020 243 249 http://www.kjm-math.org/article_109821_13bebfe55715bbb4a8fec12a006e6f52.pdf dx.doi.org/10.22034/kjm.2020.109821 Embedding topological spaces in a type of generalized topological spaces Amin Talabeigi Department of Mathematics, Payame Noor University, P.O. Box, 19395-3697, Tehran, Iran. author text article 2020 eng 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. Khayyam Journal of Mathematics 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) 2423-4788 6 v. 2 no. 2020 250 256 http://www.kjm-math.org/article_109822_48153543d90491ae26ff4e6f0859818e.pdf dx.doi.org/10.22034/kjm.2020.109822 Approximation for the Bernstein operator of max-product kind in symmetric range Ecem Acar Department of Mathematics, University of Harran, 63100, Anlurfa, Turkey author Done Karahan Department of Mathematics, University of Harran, 63100, Anlurfa, Turkey author Sevilay Kirci Serenbay Department of Mathematics, University of Harran, 63100, Anlurfa, Turkey. author text article 2020 eng 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. Khayyam Journal of Mathematics 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) 2423-4788 6 v. 2 no. 2020 257 273 http://www.kjm-math.org/article_109823_a7fe73d3f8242f905b067eb48196f51c.pdf dx.doi.org/10.22034/kjm.2020.109823