Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
Khayyam Journal of Mathematics
2423-4788
4
1
2018
01
01
Local Convergence for a Family of Sixth Order Chebyshev-Halley-Type Methods in Banach Space Under Weak Conditions
1
12
EN
Ioannis
K.
Argyros
Department of Mathematical Sciences, Cameron University, Lawton, OK
73505, USA.
iargyros@cameron.edu
Santhosh
George
Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India-575 025.
sgeorge@nitk.ac.in
10.22034/kjm.2017.51873
We present a local convergence analysis for a family of super-Halley methods of high convergence order in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first and second <span>Fréchet</span>-derivative of the operator involved. Earlier studies use hypotheses up to the third <span>Fréchet-</span>derivative. Numerical examples are also provided in this study.
Chebyshev-Halley method,Banach space,local convergence,radius of convergence,Fréchet-derivative
http://www.kjm-math.org/article_51873.html
http://www.kjm-math.org/article_51873_01211642c310828d7695de3477fc151d.pdf
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
Khayyam Journal of Mathematics
2423-4788
4
1
2018
01
01
The Second Symmetric Product of Finite Graphs from a Homotopical Viewpoint
13
27
EN
José G.
Anaya
Facultad de Ciencias, Universidad Autónoma del Estado de México, Instituto
Literario No. 100, Col. Centro, C. P. 50000, Toluca, México.
jgao@uaemex.mx
Alfredo
Cano
Facultad de Ciencias, Universidad Autónoma del Estado de México, Instituto
Literario No. 100, Col. Centro, C. P. 50000, Toluca, México.
calfredo420@gmail.com
Enrique
Castañeda-Alvarado
0000-0002-4393-2348
Facultad de Ciencias, Universidad Autónoma del Estado de México, Instituto
Literario No. 100, Col. Centro, C. P. 50000, Toluca, México.
eca@uaemex.mx
Marco A.
Castillo-Rubí
Facultad de Ciencias, Universidad Autónoma del Estado de México, Instituto
Literario No. 100, Col. Centro, C. P. 50000, Toluca, México.
eulerubi@yahoo.com.mx
10.22034/kjm.2017.53432
This paper describes the classification of the $n$-fold symmetric product of a finite graph by means of its homotopy type, having as universal models the $n$-fold symmetric product of the wedge of $n$-circles; and introduces a CW-complex called $binomial torus$, which is homeomorphic to a space that is a strong deformation retract of the second symmetric products of the wedge of $n$-circles. Applying the above we calculate the fundamental group, Euler characteristic, homology and cohomology groups of the second symmetric product of finite graphs.
Hyperspaces,symmetric product,finite graph,homotopy
http://www.kjm-math.org/article_53432.html
http://www.kjm-math.org/article_53432_e889f317edc114515e2bb1d54c2de580.pdf
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
Khayyam Journal of Mathematics
2423-4788
4
1
2018
01
01
A Subclass of Harmonic Univalent Functions Defined by Means of Differential Subordination
28
38
EN
Serkan
Çakmak
Department of Mathematics, Faculty of Arts and Science, Uludag University, 16059, Görükle, Bursa, Turkey.
serkan.cakmak64@gmail.com
Sibel
Yalçın
Department of Mathematics, Faculty of Arts and Science, Uludag University, 16059, Görükle, Bursa, Turkey.
syalcin@uludag.edu.tr
Şahsene
Altinkaya
Department of Mathematics, Faculty of Arts and Science, Uludag University, 16059, Görükle, Bursa, Turkey.
sahsene@uludag.edu.tr
10.22034/kjm.2017.53655
The aim of this paper is to introduce a new class of harmonic functions<br />defined by use of a subordination. We find necessary and sufficient<br />conditions, radii of starlikeness and convexity and compactness for this<br />class of functions. Moreover, by using extreme points theory we also obtain<br />coefficients estimates, distortion theorems for this class of functions. On<br />the other hand, some results (corollaries) on the paper are pointed out.
Harmonic functions,univalent functions,modified Su{a}lu{a}gean operator,subordination
http://www.kjm-math.org/article_53655.html
http://www.kjm-math.org/article_53655_37704e2531cb2f56dc09561deff132ef.pdf
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
Khayyam Journal of Mathematics
2423-4788
4
1
2018
01
01
Ostrowski Type Fractional Integral Operators for Generalized Beta $(r,g)$-Preinvex Functions
39
58
EN
Artion
Kashuri
0000-0003-0115-3079
Department of Mathematics, Faculty of Technical Science, University ”Ismail
Qemali”, Vlora, Albania.
artionkashuri@gmail.com
Rozana
Liko
Department of Mathematics, Faculty of Technical Science, University ”Ismail
Qemali”, Vlora, Albania.
rozanaliko86@gmail.com
Tingsong
Du
College of Science, China Three Gorges University, 443002, Yichang, P. R.
China.
tingsongdu@ctgu.edu.cn
10.22034/kjm.2017.54680
In the present paper, the notion of generalized beta $(r,g)$-preinvex function is applied for establish some new generalizations of Ostrowski type inequalities via fractional integral operators. These results not only extend the results appeared in the literature [43] but also provide new estimates on these type. At the end, some applications to special means are given.
Ostrowski type inequality,Hölder's inequality,Minkowski's inequality,power mean inequality,Riemann-Liouville fractional integral,fractional integral operator,$s$-convex function in the second sense,$m$-invex
http://www.kjm-math.org/article_54680.html
http://www.kjm-math.org/article_54680_ff16555c24403f6b3496ce50c6fd8bbf.pdf
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
Khayyam Journal of Mathematics
2423-4788
4
1
2018
01
01
Constructing an Element of a Banach Space with Given Deviation from its Nested Subspaces
59
76
EN
Asuman
Aksoy
Department of Mathematics, Claremont McKenna College, 850 Columbia Avenue, Claremont, CA 91711, USA.
aaksoy@cmc.edu
Qidi
Peng
Institute of Mathematical Sciences, Claremont Graduate University, 710 N.
College Avenue, Claremont, CA 91711, USA.
qidi.peng@cgu.edu
10.22034/kjm.2018.55158
This paper contains two improvements on a theorem of S. N. Bernstein for Banach spaces. We show that if $X$ is an arbitrary infinite-dimensional Banach space, ${Y_n}$ is a sequence of strictly nested subspaces of $ X$ and if ${d_n}$ is a non-increasing sequence of non-negative numbers tending to 0, then for any $cin(0,1]$<br /> we can find $x_{c} in X$, such that the distance $rho(x_{c}, Y_n)$ from $x_{c}$ to $Y_n$ satisfies<br />$$<br />c d_n leq rho(x_{c},Y_n) leq 4c d_n,~mbox{for all $ninmathbb N$}.<br />$$<br />We prove the above inequality by first improving Borodin (2006)'s result for Banach spaces by weakening his condition on the sequence ${d_n}$. The weakened condition on $d_n$ requires refinement of Borodin's construction to extract an element in $X$, whose distances from the nested subspaces are precisely the given values $d_n$.
Best approximation,Bernstein's lethargy theorem,Banach space,Hahn-Banach theorem
http://www.kjm-math.org/article_55158.html
http://www.kjm-math.org/article_55158_6967a156928a4b5003d50eae0fedc911.pdf
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
Khayyam Journal of Mathematics
2423-4788
4
1
2018
01
01
Laplacian and Signless Laplacian Spectrum of Commuting Graphs of Finite Groups
77
87
EN
Jutirekha
Dutta
Department of Mathematical Sciences, Tezpur University, Napaam-784028,
Sonitpur, Assam, India.
jutirekhadutta@yahoo.com
Rajat
Kanti
Nath
Department of Mathematical Sciences, Tezpur University, Napaam-784028,
Sonitpur, Assam, India.
rajatkantinath@yahoo.com
10.22034/kjm.2018.57490
The commuting graph of a finite non-abelian group $G$ with center $Z(G)$, denoted by $Gamma_G$, is a simple undirected graph whose vertex set is $Gsetminus Z(G)$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy = yx$.<br />A finite non-abelian group $G$ is called super integral if the spectrum, Laplacian spectrum and signless Laplacian spectrum of its commuting graph contain only integers.<br />In this paper, we first compute Laplacian spectrum and signless Laplacian spectrum of several families of finite non-abelian groups and conclude that those groups are super integral. As an application of our results we obtain<br />some positive rational numbers $r$ such that $G$ is super integral if commutativity degree of $G$ is $r$. In the last section, we show that $G$ is super integral if $G$ is not isomorphic to $S_4$ and its commuting graph is planar. We conclude the paper showing that $G$ is super integral if its commuting graph is toroidal.
Commuting graph,spectrum,integral graph,finite group
http://www.kjm-math.org/article_57490.html
http://www.kjm-math.org/article_57490_293c3a034fe521dab3aecbbd7b850f8f.pdf
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
Khayyam Journal of Mathematics
2423-4788
4
1
2018
01
01
Polynomial Bounds for a Class of Univalent Function Involving Sigmoid Function
88
101
EN
Olubunmi
A.
Fadipe-Joseph
0000-0001-7781-6807
Department of Mathematics, University of Ilorin, P.M.B. 1515 Ilorin,
Nigeria.
famelov@gmail.com
Bilikis
B.
Kadir
Department of Mathematics, University of Ilorin, P.M.B. 1515 Ilorin,
Nigeria.
bilkiskadir@gmail.com
Sunday
E.
Akinwumi
Department of Mathematics, University of Ilorin, P.M.B. 1515 Ilorin,
Nigeria.
olusundey@yahoo.com
Esther
O.
Adeniran
Department of Mathematics, University of Ilorin, P.M.B. 1515 Ilorin,
Nigeria.
yemisioduwole1@gmail.com
10.22034/kjm.2018.57721
In this work, a new subclass of univalent function was defined using the <span>Sălăgean</span> differential operator involving the modified sigmoid function and the Chebyshev polynomials. The coefficient bounds and the Fekete-Szego functional of this class were obtained using subordination principle. The results obtained agree and extend some earlier results.
Analytic function,Sigmoid function,Chebyshev polynomials,Sălăgean operator
http://www.kjm-math.org/article_57721.html
http://www.kjm-math.org/article_57721_db05732ca68e42ed7238c4b1cd3b3338.pdf
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
Khayyam Journal of Mathematics
2423-4788
4
1
2018
01
01
Ricci Solitons on Kenmotsu Manifolds under $D$-Homothetic Deformation
102
109
EN
Halammanavar
G.
Nagaraja
Department of Mathematics, Jnanabharathi Campus, Bangalore University,
Bengaluru, 560 056, INDIA.
hgnraj@yahoo.com
Devasandra
L.
Kiran Kumar
Department of Mathematics, Jnanabharathi Campus, Bangalore University,
Bengaluru, 560 056, INDIA.
kirankumar250791@gmail.com
Venkateshmurthy
S.
Prasad
Department of Mathematics, Regional institute of Education (NCERT), Manasagangotri, Mysore, 570006, INDIA.
vspriem@gmail.com
10.22034/kjm.2018.57725
The aim of the present paper is to study Ricci solitons in Kenmotsu manifolds under $D$-homothetic deformation. We analyzed behaviour of Ricci solitons when potential vector field is orthogonal to Reeb vector field and pointwise collinear with Reeb vector field. Further we prove Ricci solitons in $D$-homothetically transformed Kenmotsu manifolds are shrinking.
http://www.kjm-math.org/article_57725.html
http://www.kjm-math.org/article_57725_899a6e6b876f185709cce8565826c41a.pdf