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 Mathematics2423-47886120200101On a New Class of Bernstein Type Operators Based on Beta Function1159709010.22034/kjm.2019.97090ENDhawal J.BhattApplied Mathematics and Humanities Department, Sardar Vallabhbhai National Institute of Technology, Ichchhanath Mahadev Dumas Road, Surat-395
007 (Gujarat), India.Vishnu NarayanMishraDepartment of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, (Madhya Pradesh)- 484 887, India.0000-0002-2159-7710Ranjan KumarJanaApplied Mathematics and Humanities Department, Sardar Vallabhbhai National Institute of Technology, Ichchhanath Mahadev Dumas Road, Surat-395
007 (Gujarat), India.Journal Article20190415We develop Bernstein type operators using the Beta function and study their approximation properties. By using Korovkin's theorem, we achieve the uniform convergence of sequences of these operators. We obtain the rate of convergence in terms of modulus of continuity and establish the Voronovskaja type asymptotic result for these operators. At last the graphical comparison of these newly defined operators with few of the fundamental but significant operators is discussed.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 Mathematics2423-47886120200101Invariant Submanifolds of LP-Sasakian Manifolds16269709110.22034/kjm.2019.97091ENVenkateshaVenkateshaDepartment of Mathematics, Kuvempu University, Shankaraghatta-577451, Karnataka, India.0000-0002-2799-2535ShanmukhaBasavarajappaDepartment of Mathematics, Kuvempu University, Shankaraghatta-577451, Karnataka, India.Journal Article20180921The object of the present paper is to study some geometric conditions for an invariant submanifold of an LP-Sasakian manifold to be totally geodesic. Further we consider concircular curvature tensor satisfying some geometric conditions of an invariant submanifold of an LP-Sasakian manifold to be totally geodesic. In extension, we build an example of LP-Sasakian manifold to verify our main result totally geodesic.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 Mathematics2423-47886120200101Various Energies of Commuting Graphs of Finite Nonabelian Groups27459709410.22034/kjm.2019.97094ENParamaDuttaDepartment of Mathematical Sciences, Tezpur University, Napaam 784028, Sonitpur, Assam, India.BiswadeepBagchiDepartment of Mathematical Sciences, Tezpur University, Napaam 784028, Sonitpur, Assam, India.Rajat KantiNathDepartment of Mathematical Sciences, Tezpur University, Napaam 784028, Sonitpur, Assam, India.Journal Article20181123The commuting graph of a finite nonabelian group $G$ is a simple undirected graph, denoted by $Gamma_G$, whose vertex set is the noncentral elements of $G$ and two distinct vertices $x$ and $y$ are adjacent if and only if $xy = yx$. In this paper, we compute energy, Laplacian energy, and signless Laplacian energy of $Gamma_G$ for various families of finite nonabelian groups and analyze their values graphically. Our computations show that the conjecture posed in [MATCH Commun. Math. Comput. Chem. 59, (2008) 343-354 ] holds for the commuting graph of some families of finite groups.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 Mathematics2423-47886120200101Some Properties of Prime and Z-Semi-Ideals in Posets46569709510.22034/kjm.2019.97095ENKasiPorselviDepartment of Mathematics, Karunya Institute of Technology and Sciences,
Coimbatore - 641 114, India.BalasubramanianElavarasanDepartment of Mathematics, Karunya Institute of Technology and Sciences,
Coimbatore - 641 114, India.0000-0002-1414-2814Journal Article20181201We define the notion of z-semi-ideals in a poset $P$ and we show that if a z-semi-ideal $J$ satisfies $(ast )$-property, then every minimal prime semi-ideal containing $J$ is also a z-semi-ideal of $P.$ We also show that every prime semi-ideal is a z-semi-ideal or the maximal z-semi-ideals contained in it are prime z-semi-ideals. Further, we characterize some properties of union of prime semi-ideals of $P$ provided the prime semi-ideals are contained in the unique maximal semi-ideal of $P.$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 Mathematics2423-47886120200101Strongly Quasilinear Parabolic Systems in Divergence Form with Weak Monotonicity57729717010.22034/kjm.2019.97170ENElhoussineAzroulDepartment of Mathematics, Faculty of Sciences Dhar El Mehraz, B.P. 1796 Atlas, Fez-Morocco.FarahBalaadichDepartment of Mathematics, Faculty of Sciences Dhar El Mehraz, B.P. 1796 Atlas, Fez-Morocco.Journal Article20181205The existence of solutions to the strongly quasilinear parabolic system<br />[frac{partial u}{partial t}-text{div},sigma(x,t,u,Du)+g(x,t,u,Du)=f,]<br />is proved, where the source term $f$ is assumed to belong to $L^{p'}(0,T; W^{-1,p'}(Omega;R^m))$. Further, we prove the existence of a weak solution by means of the Young measures under mild monotonicity assumptions on $sigma$.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 Mathematics2423-47886120200101On Approximation of Functions Belonging to some Classes of Functions by $(N,p_n,q_n)(E,theta )$ Means of Conjugate Series of Its Fourier Series73869717310.22034/kjm.2019.97173ENXhevat ZahirKrasniqiUniversity of Prishtina "Hasan Prishtina", Faculty of Education, Department of Mathematics and Informatics, Avenue "Mother Theresa" 5, 10000 Prishtina, Kosovo.Deepmala-Mathematics Discipline, PDPM Indian Institute of Information Technology,
Design and Manufacturing, Jabalpur, Dumna Airport Road, P.O.: Khamaria,
Jabalpur 482 005, Madhya Pradesh, India.Journal Article20181210We obtain some new results on the approximation of functions belonging to some classes of functions by $(N,p_n,q_n)(E,theta )$ means of conjugate series of its Fourier series. These results, under conditions assumed here, are better than those obtained previously by others. In addition, several particular results are derived from our results as corollaries.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 Mathematics2423-47886120200101On Pair of Generalized Derivations in Rings87949717410.22034/kjm.2019.97174ENAsmaAliDepartment of Mathematics, Aligarh Muslim University, Aligarh-202002,
India.Md HamidurRahamanDepartment of Mathematics, Aligarh Muslim University, Aligarh-202002,
India.Journal Article20181212Let $R$ be an associative ring with extended centroid $C$, let $G$ and $F$ be generalized derivations of $R$ associated with nonzero derivations $delta$ and $d$, respectively, and let $m, k, n geq1$ be fixed integers. In the present paper, we study the situations: (i)$F(x)circ_{m}G(y)=(x circ_{n} y)^{k}$, (ii) $[F(x),y]_{m}+[x,d(y)]_{n}=0$ for all $y, x$ in some appropriate subset of $R$.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 Mathematics2423-47886120200101Approximating Solutions of Third-Order Nonlinear Hybrid Differential Equations via Dhage Iteration Principle951039717510.22034/kjm.2019.97175ENAbdelouahebArdjouniFaculty of Sciences and Technology, Department of Mathematics and Informatics, Souk Ahras University, P.O. Box 1553, Souk Ahras, 41000, Algeria.AhceneDjoudiApplied Mathematics Lab, Faculty of Sciences, Department of Mathematics,
Annaba University, P.O. Box 12, Annaba, 23000, Algeria.Journal Article20190102We prove the existence and approximation of solutions of the initial value problems of nonlinear third-order hybrid differential equations. The main tool employed here is the Dhage iteration principle in a partially ordered normed linear space. An example is also given to illustrate the main results.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 Mathematics2423-47886120200101On the Norm of Jordan $*$-Derivations1041079717610.22034/kjm.2019.97176ENAbolfazlNiazi MotlaghDepartment of Mathematics, Faculty of basic sciences, University of Bojnord,
P.O. Box 1339, Bojnord, Iran.Journal Article20190121Let $mathcal H$ be a complex Hilbert space and let $B(mathcal H)$ be the algebra of all bounded linear operators on $mathcal H$. Let $Tin B(mathcal H)$.<br />In this paper, we determine the norm of the inner Jordan $*$-derivation $Delta_T:Xmapsto TX-X^*T$ acting on the Banach algebra $B(mathcal{H})$. More precisely, we show that $$big{|}Delta_Tbig{|}geq 2sup_{lambdain W_0(T)}|{rm Im}(lambda)|$$<br />in which $W_0(T)$ is the maximal numerical range of operator $T$.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 Mathematics2423-47886120200101Commuting Conjugacy Class Graph of Finite CA-Groups1081189717710.22034/kjm.2019.97177ENMohammad AliSalahshourDepartment of Pure Mathematics, University of Kashan, Kashan 87317-53153, Iran.Ali RezaAshrafiDepartment of Pure Mathematics, University of Kashan, Kashan 87317-53153, Iran.Journal Article20190215Let $G$ be a finite nonabelian group. The commuting conjugacy class graph $Gamma(G)$ is a simple graph with the noncentral conjugacy classes of $G$ as its vertex set and two distinct vertices $X$ and $Y$ in $Gamma(G)$ are adjacent if and only if there are $x in X$ and $y in Y$ with this property that $xy = yx$. The aim of this paper is to obtain the structure of the commuting conjugacy class graph of finite CA-groups. It is proved that this graph is a union of some complete graphs. The commuting conjugacy class graph of certain groups are also computed.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 Mathematics2423-47886120200101On Jensen's Multiplicative Inequality for Positive Convex Functions of Selfadjoint Operators in Hilbert Spaces1191289718310.22034/kjm.2019.97183ENSilvestru SeverDragomirMathematics, College of Engineering & Science, Victoria University, PO
Box 14428, Melbourne City, MC 8001, Australia.0000-0003-2902-6805Journal Article20190501We obtain some multiplicative refinements and reverses of Jensen's inequality for positive convex/concave functions of selfadjoint operators in Hilbert spaces. Natural applications for power and exponential functions are provided.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 Mathematics2423-47886120200101On Gluing of Quasi-Pseudometric Spaces1291409719310.22034/kjm.2019.97193ENYolandaMutemwaSchool of Mathematical Sciences, North-West University (Mafikeng Campus), Private Bag X2046, Mmabatho 2735, South Africa.Olivier OlelaOtafuduSchool of Mathematics, University of the Witwatersrand Johannesburg
2050, South Africa.0000-0001-9593-7899HopeSabaoSchool of Mathematics, University of the Witwatersrand Johannesburg
2050, South Africa.0000-0002-8649-5635Journal Article20190905The concept of gluing a family of $T_0$-quasi-metric spaces along subsets was introduced by Otafudu. In this article, we continue the study of externally Isbell-convex and weakly externally Isbell-convex subsets of a $T_0$-quasi-metric space. We finally investigate some properties of the resulting $T_0$-quasi-metric space obtained by gluing a family of Isbell-convex $T_0$-quasi-metric spaces attached<br />along isometric subspaces.