eng
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
2423-4788
2020-01-01
6
1
1
15
10.22034/kjm.2019.97090
97090
On a New Class of Bernstein Type Operators Based on Beta Function
Dhawal Bhatt
dhawal.bhatt@sxca.edu.in
1
Vishnu Mishra
vishnunarayanmishra@gmail.com
2
Ranjan Jana
rkjana2003@yahoo.com
3
Applied Mathematics and Humanities Department, Sardar Vallabhbhai National Institute of Technology, Ichchhanath Mahadev Dumas Road, Surat-395 007 (Gujarat), India.
Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, (Madhya Pradesh)- 484 887, India.
Applied Mathematics and Humanities Department, Sardar Vallabhbhai National Institute of Technology, Ichchhanath Mahadev Dumas Road, Surat-395 007 (Gujarat), India.
We 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.
http://www.kjm-math.org/article_97090_cadb0c8d0798a9820fa3976ce509413e.pdf
Beta function
Korovkin theorem
Modulus of continuity
Voronovskaya type result
eng
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
2423-4788
2020-01-01
6
1
16
26
10.22034/kjm.2019.97091
97091
Invariant Submanifolds of LP-Sasakian Manifolds
Venkatesha Venkatesha
vensmath@gmail.com
1
Shanmukha Basavarajappa
meshanmukha@gmail.com
2
Department of Mathematics, Kuvempu University, Shankaraghatta-577451, Karnataka, India.
Department of Mathematics, Kuvempu University, Shankaraghatta-577451, Karnataka, India.
The 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.
http://www.kjm-math.org/article_97091_d52712c3a0533f86645740d2df993eba.pdf
Submanifold
LP-Sasakian manifold
concircular curvature tensor
eng
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
2423-4788
2020-01-01
6
1
27
45
10.22034/kjm.2019.97094
97094
Various Energies of Commuting Graphs of Finite Nonabelian Groups
Parama Dutta
parama@gonitsora.com
1
Biswadeep Bagchi
biswadeepbagchi430@gmail.com
2
Rajat Nath
rajatkantinath@yahoo.com
3
Department of Mathematical Sciences, Tezpur University, Napaam 784028, Sonitpur, Assam, India.
Department of Mathematical Sciences, Tezpur University, Napaam 784028, Sonitpur, Assam, India.
Department of Mathematical Sciences, Tezpur University, Napaam 784028, Sonitpur, Assam, India.
The 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.
http://www.kjm-math.org/article_97094_19bea7eef79e328fcdc7ad5118452748.pdf
Commuting graph
spectrum
Energy
finite group
eng
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
2423-4788
2020-01-01
6
1
46
56
10.22034/kjm.2019.97095
97095
Some Properties of Prime and Z-Semi-Ideals in Posets
Kasi Porselvi
porselvi94@yahoo.co.in
1
Balasubramanian Elavarasan
belavarasan@gmail.com
2
Department of Mathematics, Karunya Institute of Technology and Sciences, Coimbatore - 641 114, India.
Department of Mathematics, Karunya Institute of Technology and Sciences, Coimbatore - 641 114, India.
We 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 $P.$
http://www.kjm-math.org/article_97095_c7b4d571f0807aca269c3e30f1b3b35f.pdf
Posets
semi-ideals
prime semi-ideals
minimal prime semi-ideals
m-system
eng
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
2423-4788
2020-01-01
6
1
57
72
10.22034/kjm.2019.97170
97170
Strongly Quasilinear Parabolic Systems in Divergence Form with Weak Monotonicity
Elhoussine Azroul
elhoussine.azroul@gmail.com
1
Farah Balaadich
balaadich.edp@gmail.com
2
Department of Mathematics, Faculty of Sciences Dhar El Mehraz, B.P. 1796 Atlas, Fez-Morocco.
Department of Mathematics, Faculty of Sciences Dhar El Mehraz, B.P. 1796 Atlas, Fez-Morocco.
The 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 $sigma$.
http://www.kjm-math.org/article_97170_c50bb41e07dca9346043d4702bb0d0b2.pdf
Quasilinear parabolic systems
weak monotonicity
weak solution
Young measures
eng
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
2423-4788
2020-01-01
6
1
73
86
10.22034/kjm.2019.97173
97173
On 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
Xhevat Krasniqi
xhevat.krasniqi@uni-pr.edu
1
Deepmala -
dmrai23@gmail.com
2
University of Prishtina "Hasan Prishtina", Faculty of Education, Department of Mathematics and Informatics, Avenue "Mother Theresa" 5, 10000 Prishtina, Kosovo.
Mathematics Discipline, PDPM Indian Institute of Information Technology, Design and Manufacturing, Jabalpur, Dumna Airport Road, P.O.: Khamaria, Jabalpur 482 005, Madhya Pradesh, India.
We 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.
http://www.kjm-math.org/article_97173_e5cbb8cc4f0476c8532b33b6a744e7ab.pdf
Fourier series
generalized N"{o}rlund means
conjugate Fourier series
degree of approximation
eng
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
2423-4788
2020-01-01
6
1
87
94
10.22034/kjm.2019.97174
97174
On Pair of Generalized Derivations in Rings
Asma Ali
asma_ali2@rediffmail.com
1
Md Rahaman
rahamanhamidmath@gmail.com
2
Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India.
Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India.
Let $R$ 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 $R$.
http://www.kjm-math.org/article_97174_d6600441ebda02c760dafc2171b8c9a6.pdf
Prime rings
semiprime rings
generalized derivations
extended centroid
eng
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
2423-4788
2020-01-01
6
1
95
103
10.22034/kjm.2019.97175
97175
Approximating Solutions of Third-Order Nonlinear Hybrid Differential Equations via Dhage Iteration Principle
Abdelouaheb Ardjouni
abd_ardjouni@yahoo.fr
1
Ahcene Djoudi
adjoudi@yahoo.com
2
Faculty of Sciences and Technology, Department of Mathematics and Informatics, Souk Ahras University, P.O. Box 1553, Souk Ahras, 41000, Algeria.
Applied Mathematics Lab, Faculty of Sciences, Department of Mathematics, Annaba University, P.O. Box 12, Annaba, 23000, Algeria.
We 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.
http://www.kjm-math.org/article_97175_4f0895cb4388259d8103049f6f6095a4.pdf
Approximating solutions
Initial value problems
Dhage iteration principle
hybrid fixed point theorem
eng
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
2423-4788
2020-01-01
6
1
104
107
10.22034/kjm.2019.97176
97176
On the Norm of Jordan $*$-Derivations
Abolfazl Niazi Motlagh
niazimotlagh@gmail.com
1
Department of Mathematics, Faculty of basic sciences, University of Bojnord, P.O. Box 1339, Bojnord, Iran.
Let $mathcal H$ 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 $T$.
http://www.kjm-math.org/article_97176_b3a4d842feb70c384bb0001e22fc2e2b.pdf
Jordan$*$-derivation
Numerical Range
maximal numerical range
eng
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
2423-4788
2020-01-01
6
1
108
118
10.22034/kjm.2019.97177
97177
Commuting Conjugacy Class Graph of Finite CA-Groups
Mohammad Salahshour
salahshour@iausk.ac.ir
1
Ali Ashrafi
ashrafi_1385@yahoo.co.in
2
Department of Pure Mathematics, University of Kashan, Kashan 87317-53153, Iran.
Department of Pure Mathematics, University of Kashan, Kashan 87317-53153, Iran.
Let $G$ 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.
http://www.kjm-math.org/article_97177_3bc76fe226764a53f2b1071b15cca234.pdf
Commuting conjugacy class graph
Commuting graph
CA-group
quotient graph
eng
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
2423-4788
2020-01-01
6
1
119
128
10.22034/kjm.2019.97183
97183
On Jensen's Multiplicative Inequality for Positive Convex Functions of Selfadjoint Operators in Hilbert Spaces
Silvestru Dragomir
sever.dragomir@vu.edu.au
1
Mathematics, College of Engineering & Science, Victoria University, PO Box 14428, Melbourne City, MC 8001, Australia.
We 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.
http://www.kjm-math.org/article_97183_0bab1e1807c57ade01a6dbcdeaa87638.pdf
Young's Inequality
Convex functions
Jensen's inequality
Selfadjoint operator
functions of selfadjoint operators
eng
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
2423-4788
2020-01-01
6
1
129
140
10.22034/kjm.2019.97193
97193
On Gluing of Quasi-Pseudometric Spaces
Yolanda Mutemwa
yolanda.mutemwa@gmail.com
1
Olivier Otafudu
olivier.olelaotafudu@wits.ac.za
2
Hope Sabao
hope.sabao@wits.ac.za
3
School of Mathematical Sciences, North-West University (Mafikeng Campus), Private Bag X2046, Mmabatho 2735, South Africa.
School of Mathematics, University of the Witwatersrand Johannesburg 2050, South Africa.
School of Mathematics, University of the Witwatersrand Johannesburg 2050, South Africa.
The 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.
http://www.kjm-math.org/article_97193_f40ec285c7f66495a0dc6501643590b4.pdf
Isbell-convexity
gluing quasi-pseudometric
externally Isbell-convexity