2018-07-21T23:49:52Z
http://www.kjm-math.org/?_action=export&rf=summon&issue=7188
Khayyam Journal of Mathematics
Khayyam J. Math.
2018
4
1
Local Convergence for a Family of Sixth Order Chebyshev-Halley-Type Methods in Banach Space Under Weak Conditions
Ioannis
Argyros
Santhosh
George
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.
Chebyshev-Halley method
Banach space
local convergence
radius of convergence
Fréchet-derivative
2018
01
01
1
12
http://www.kjm-math.org/article_51873_01211642c310828d7695de3477fc151d.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2018
4
1
The Second Symmetric Product of Finite Graphs from a Homotopical Viewpoint
José G.
Anaya
Alfredo
Cano
Enrique
Castañeda-Alvarado
Marco A.
Castillo-Rubí
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
2018
01
01
13
27
http://www.kjm-math.org/article_53432_e889f317edc114515e2bb1d54c2de580.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2018
4
1
A Subclass of Harmonic Univalent Functions Defined by Means of Differential Subordination
Serkan
Çakmak
Sibel
Yalçın
Şahsene
Altinkaya
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.
Harmonic functions
univalent functions
modified Su{a}lu{a}gean operator
subordination
2018
01
01
28
38
http://www.kjm-math.org/article_53655_37704e2531cb2f56dc09561deff132ef.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2018
4
1
Ostrowski Type Fractional Integral Operators for Generalized Beta $(r,g)$-Preinvex Functions
Artion
Kashuri
Rozana
Liko
Tingsong
Du
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
2018
01
01
39
58
http://www.kjm-math.org/article_54680_ff16555c24403f6b3496ce50c6fd8bbf.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2018
4
1
Constructing an Element of a Banach Space with Given Deviation from its Nested Subspaces
Asuman
Aksoy
Qidi
Peng
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 $d_n$.
Best approximation
Bernstein's lethargy theorem
Banach space
Hahn-Banach theorem
2018
01
01
59
76
http://www.kjm-math.org/article_55158_6967a156928a4b5003d50eae0fedc911.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2018
4
1
Laplacian and Signless Laplacian Spectrum of Commuting Graphs of Finite Groups
Jutirekha
Dutta
Rajat
Nath
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.
Commuting graph
spectrum
integral graph
finite group
2018
01
01
77
87
http://www.kjm-math.org/article_57490_293c3a034fe521dab3aecbbd7b850f8f.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2018
4
1
Polynomial Bounds for a Class of Univalent Function Involving Sigmoid Function
Olubunmi
Fadipe-Joseph
Bilikis
Kadir
Sunday
Akinwumi
Esther
Adeniran
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.
Analytic function
Sigmoid function
Chebyshev polynomials
Sălăgean operator
2018
01
01
88
101
http://www.kjm-math.org/article_57721_db05732ca68e42ed7238c4b1cd3b3338.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2018
4
1
Ricci Solitons on Kenmotsu Manifolds under $D$-Homothetic Deformation
Halammanavar
Nagaraja
Devasandra
Kiran Kumar
Venkateshmurthy
Prasad
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.
2018
01
01
102
109
http://www.kjm-math.org/article_57725_899a6e6b876f185709cce8565826c41a.pdf