eng
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
2423-4788
2018-01-01
4
1
1
12
10.22034/kjm.2017.51873
51873
Local Convergence for a Family of Sixth Order Chebyshev-Halley-Type Methods in Banach Space Under Weak Conditions
Ioannis Argyros
iargyros@cameron.edu
1
Santhosh George
sgeorge@nitk.ac.in
2
Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA.
Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India-575 025.
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 Fréchet-derivative of the operator involved. Earlier studies use hypotheses up to the third Fréchet-derivative. Numerical examples are also provided in this study.
http://www.kjm-math.org/article_51873_01211642c310828d7695de3477fc151d.pdf
Chebyshev-Halley method
Banach space
local convergence
radius of convergence
Fréchet-derivative
eng
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
2423-4788
2018-01-01
4
1
13
27
10.22034/kjm.2017.53432
53432
The Second Symmetric Product of Finite Graphs from a Homotopical Viewpoint
José G. Anaya
jgao@uaemex.mx
1
Alfredo Cano
calfredo420@gmail.com
2
Enrique Castañeda-Alvarado
eca@uaemex.mx
3
Marco A. Castillo-Rubí
eulerubi@yahoo.com.mx
4
Facultad de Ciencias, Universidad Autónoma del Estado de México, Instituto Literario No. 100, Col. Centro, C. P. 50000, Toluca, México.
Facultad de Ciencias, Universidad Autónoma del Estado de México, Instituto Literario No. 100, Col. Centro, C. P. 50000, Toluca, México.
Facultad de Ciencias, Universidad Autónoma del Estado de México, Instituto Literario No. 100, Col. Centro, C. P. 50000, Toluca, México.
Facultad de Ciencias, Universidad Autónoma del Estado de México, Instituto Literario No. 100, Col. Centro, C. P. 50000, Toluca, México.
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.
http://www.kjm-math.org/article_53432_e889f317edc114515e2bb1d54c2de580.pdf
Hyperspaces
symmetric product
finite graph
homotopy
eng
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
2423-4788
2018-01-01
4
1
28
38
10.22034/kjm.2017.53655
53655
A Subclass of Harmonic Univalent Functions Defined by Means of Differential Subordination
Serkan Çakmak
serkan.cakmak64@gmail.com
1
Sibel Yalçın
syalcin@uludag.edu.tr
2
Şahsene Altinkaya
sahsene@uludag.edu.tr
3
Department of Mathematics, Faculty of Arts and Science, Uludag University, 16059, Görükle, Bursa, Turkey.
Department of Mathematics, Faculty of Arts and Science, Uludag University, 16059, Görükle, Bursa, Turkey.
Department of Mathematics, Faculty of Arts and Science, Uludag University, 16059, Görükle, Bursa, Turkey.
The aim of this paper is to introduce a new class of harmonic functionsdefined by use of a subordination. We find necessary and sufficientconditions, radii of starlikeness and convexity and compactness for thisclass of functions. Moreover, by using extreme points theory we also obtaincoefficients estimates, distortion theorems for this class of functions. Onthe other hand, some results (corollaries) on the paper are pointed out.
http://www.kjm-math.org/article_53655_37704e2531cb2f56dc09561deff132ef.pdf
Harmonic functions
univalent functions
modified Su{a}lu{a}gean operator
subordination
eng
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
2423-4788
2018-01-01
4
1
39
58
10.22034/kjm.2017.54680
54680
Ostrowski Type Fractional Integral Operators for Generalized Beta $(r,g)$-Preinvex Functions
Artion Kashuri
artionkashuri@gmail.com
1
Rozana Liko
rozanaliko86@gmail.com
2
Tingsong Du
tingsongdu@ctgu.edu.cn
3
Department of Mathematics, Faculty of Technical Science, University ”Ismail Qemali”, Vlora, Albania.
Department of Mathematics, Faculty of Technical Science, University ”Ismail Qemali”, Vlora, Albania.
College of Science, China Three Gorges University, 443002, Yichang, P. R. China.
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.
http://www.kjm-math.org/article_54680_ff16555c24403f6b3496ce50c6fd8bbf.pdf
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
eng
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
2423-4788
2018-01-01
4
1
59
76
10.22034/kjm.2018.55158
55158
Constructing an Element of a Banach Space with Given Deviation from its Nested Subspaces
Asuman Aksoy
aaksoy@cmc.edu
1
Qidi Peng
qidi.peng@cgu.edu
2
Department of Mathematics, Claremont McKenna College, 850 Columbia Avenue, Claremont, CA 91711, USA.
Institute of Mathematical Sciences, Claremont Graduate University, 710 N. College Avenue, Claremont, CA 91711, USA.
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 $cin(0,1]$ we can find $x_{c} in X$, such that the distance $rho(x_{c}, Y_n)$ from $x_{c}$ to $Y_n$ satisfies$$c d_n leq rho(x_{c},Y_n) leq 4c d_n,~mbox{for all $ninmathbb N$}.$$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 $d_n$.
http://www.kjm-math.org/article_55158_6967a156928a4b5003d50eae0fedc911.pdf
Best approximation
Bernstein's lethargy theorem
Banach space
Hahn-Banach theorem
eng
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
2423-4788
2018-01-01
4
1
77
87
10.22034/kjm.2018.57490
57490
Laplacian and Signless Laplacian Spectrum of Commuting Graphs of Finite Groups
Jutirekha Dutta
jutirekhadutta@yahoo.com
1
Rajat Nath
rajatkantinath@yahoo.com
2
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 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 $xy = yx$.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.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 obtainsome 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.
http://www.kjm-math.org/article_57490_293c3a034fe521dab3aecbbd7b850f8f.pdf
Commuting graph
spectrum
integral graph
finite group
eng
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
2423-4788
2018-01-01
4
1
88
101
10.22034/kjm.2018.57721
57721
Polynomial Bounds for a Class of Univalent Function Involving Sigmoid Function
Olubunmi Fadipe-Joseph
famelov@gmail.com
1
Bilikis Kadir
bilkiskadir@gmail.com
2
Sunday Akinwumi
olusundey@yahoo.com
3
Esther Adeniran
yemisioduwole1@gmail.com
4
Department of Mathematics, University of Ilorin, P.M.B. 1515 Ilorin, Nigeria.
Department of Mathematics, University of Ilorin, P.M.B. 1515 Ilorin, Nigeria.
Department of Mathematics, University of Ilorin, P.M.B. 1515 Ilorin, Nigeria.
Department of Mathematics, University of Ilorin, P.M.B. 1515 Ilorin, Nigeria.
In this work, a new subclass of univalent function was defined using the Sălăgean 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.
http://www.kjm-math.org/article_57721_db05732ca68e42ed7238c4b1cd3b3338.pdf
Analytic function
Sigmoid function
Chebyshev polynomials
Sălăgean operator
eng
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
2423-4788
2018-01-01
4
1
102
109
10.22034/kjm.2018.57725
57725
Ricci Solitons on Kenmotsu Manifolds under $D$-Homothetic Deformation
Halammanavar Nagaraja
hgnraj@yahoo.com
1
Devasandra Kiran Kumar
kirankumar250791@gmail.com
2
Venkateshmurthy Prasad
vspriem@gmail.com
3
Department of Mathematics, Jnanabharathi Campus, Bangalore University, Bengaluru, 560 056, INDIA.
Department of Mathematics, Jnanabharathi Campus, Bangalore University, Bengaluru, 560 056, INDIA.
Department of Mathematics, Regional institute of Education (NCERT), Manasagangotri, Mysore, 570006, INDIA.
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_899a6e6b876f185709cce8565826c41a.pdf