2018
4
1
1
109
Local Convergence for a Family of Sixth Order ChebyshevHalleyType Methods in Banach Space Under Weak Conditions
2
2
We present a local convergence analysis for a family of superHalley 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 Fréchetderivative of the operator involved. Earlier studies use hypotheses up to the third Fréchetderivative. Numerical examples are also provided in this study.
1

1
12


Ioannis
Argyros
Department of Mathematical Sciences, Cameron University, Lawton, OK
73505, USA.
Department of Mathematical Sciences, Cameron
United States
iargyros@cameron.edu


Santhosh
George
Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India575 025.
Department of Mathematical and Computational
India
sgeorge@nitk.ac.in
ChebyshevHalley method
Banach space
local convergence
radius of convergence
Fréchetderivative
The Second Symmetric Product of Finite Graphs from a Homotopical Viewpoint
2
2
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 CWcomplex 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.
1

13
27


José G.
Anaya
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
Mexico
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.
Facultad de Ciencias, Universidad Autónoma
Mexico
calfredo420@gmail.com


Enrique
CastañedaAlvarado
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
Mexico
eca@uaemex.mx


Marco A.
CastilloRubí
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
Mexico
eulerubi@yahoo.com.mx
Hyperspaces
symmetric product
finite graph
homotopy
A Subclass of Harmonic Univalent Functions Defined by Means of Differential Subordination
2
2
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.
1

28
38


Serkan
Çakmak
Department of Mathematics, Faculty of Arts and Science, Uludag University, 16059, Görükle, Bursa, Turkey.
Department of Mathematics, Faculty of Arts
Turkey
serkan.cakmak64@gmail.com


Sibel
Yalçın
Department of Mathematics, Faculty of Arts and Science, Uludag University, 16059, Görükle, Bursa, Turkey.
Department of Mathematics, Faculty of Arts
Turkey
syalcin@uludag.edu.tr


Şahsene
Altinkaya
Department of Mathematics, Faculty of Arts and Science, Uludag University, 16059, Görükle, Bursa, Turkey.
Department of Mathematics, Faculty of Arts
Turkey
sahsene@uludag.edu.tr
Harmonic functions
univalent functions
modified Su{a}lu{a}gean operator
subordination
Ostrowski Type Fractional Integral Operators for Generalized Beta $(r,g)$Preinvex Functions
2
2
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.
1

39
58


Artion
Kashuri
Department of Mathematics, Faculty of Technical Science, University ”Ismail
Qemali”, Vlora, Albania.
Department of Mathematics, Faculty of Technical
Albania
artionkashuri@gmail.com


Rozana
Liko
Department of Mathematics, Faculty of Technical Science, University ”Ismail
Qemali”, Vlora, Albania.
Department of Mathematics, Faculty of Technical
Albania
rozanaliko86@gmail.com


Tingsong
Du
College of Science, China Three Gorges University, 443002, Yichang, P. R.
China.
College of Science, China Three Gorges University,
China
tingsongdu@ctgu.edu.cn
Ostrowski type inequality
Hölder's inequality
Minkowski's inequality
power mean inequality
RiemannLiouville fractional integral
fractional integral operator
$s$convex function in the second sense
$m$invex
Constructing an Element of a Banach Space with Given Deviation from its Nested Subspaces
2
2
This paper contains two improvements on a theorem of S. N. Bernstein for Banach spaces. We show that if $X$ is an arbitrary infinitedimensional Banach space, ${Y_n}$ is a sequence of strictly nested subspaces of $ X$ and if ${d_n}$ is a nonincreasing sequence of nonnegative 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 $d_n$.
1

59
76


Asuman
Aksoy
Department of Mathematics, Claremont McKenna College, 850 Columbia Avenue, Claremont, CA 91711, USA.
Department of Mathematics, Claremont McKenna
United States
aaksoy@cmc.edu


Qidi
Peng
Institute of Mathematical Sciences, Claremont Graduate University, 710 N.
College Avenue, Claremont, CA 91711, USA.
Institute of Mathematical Sciences, Claremont
United States
qidi.peng@cgu.edu
Best approximation
Bernstein's lethargy theorem
Banach space
HahnBanach theorem
Laplacian and Signless Laplacian Spectrum of Commuting Graphs of Finite Groups
2
2
The commuting graph of a finite nonabelian 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 nonabelian 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 nonabelian 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.
1

77
87


Jutirekha
Dutta
Department of Mathematical Sciences, Tezpur University, Napaam784028,
Sonitpur, Assam, India.
Department of Mathematical Sciences, Tezpur
India
jutirekhadutta@yahoo.com


Rajat
Nath
Department of Mathematical Sciences, Tezpur University, Napaam784028,
Sonitpur, Assam, India.
Department of Mathematical Sciences, Tezpur
India
rajatkantinath@yahoo.com
Commuting graph
spectrum
integral graph
finite group
Polynomial Bounds for a Class of Univalent Function Involving Sigmoid Function
2
2
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 FeketeSzego functional of this class were obtained using subordination principle. The results obtained agree and extend some earlier results.
1

88
101


Olubunmi
FadipeJoseph
Department of Mathematics, University of Ilorin, P.M.B. 1515 Ilorin,
Nigeria.
Department of Mathematics, University of
Nigeria
famelov@gmail.com


Bilikis
Kadir
Department of Mathematics, University of Ilorin, P.M.B. 1515 Ilorin,
Nigeria.
Department of Mathematics, University of
Nigeria
bilkiskadir@gmail.com


Sunday
Akinwumi
Department of Mathematics, University of Ilorin, P.M.B. 1515 Ilorin,
Nigeria.
Department of Mathematics, University of
Nigeria
olusundey@yahoo.com


Esther
Adeniran
Department of Mathematics, University of Ilorin, P.M.B. 1515 Ilorin,
Nigeria.
Department of Mathematics, University of
Nigeria
yemisioduwole1@gmail.com
Analytic function
Sigmoid function
Chebyshev polynomials
Sălăgean operator
Ricci Solitons on Kenmotsu Manifolds under $D$Homothetic Deformation
2
2
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.
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102
109


Halammanavar
Nagaraja
Department of Mathematics, Jnanabharathi Campus, Bangalore University,
Bengaluru, 560 056, INDIA.
Department of Mathematics, Jnanabharathi
India
hgnraj@yahoo.com


Devasandra
Kiran Kumar
Department of Mathematics, Jnanabharathi Campus, Bangalore University,
Bengaluru, 560 056, INDIA.
Department of Mathematics, Jnanabharathi
India
kirankumar250791@gmail.com


Venkateshmurthy
Prasad
Department of Mathematics, Regional institute of Education (NCERT), Manasagangotri, Mysore, 570006, INDIA.
Department of Mathematics, Regional institute
India
vspriem@gmail.com