Local Convergence for a Family of Sixth Order Chebyshev-Halley-Type Methods in Banach Space Under Weak Conditions
Ioannis
Argyros
Department of Mathematical Sciences, Cameron University, Lawton, OK
73505, USA.
author
Santhosh
George
Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India-575 025.
author
text
article
2018
eng
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.
Khayyam Journal of Mathematics
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)
2423-4788
4
v.
1
no.
2018
1
12
http://www.kjm-math.org/article_51873_01211642c310828d7695de3477fc151d.pdf
dx.doi.org/10.22034/kjm.2017.51873
The Second Symmetric Product of Finite Graphs from a Homotopical Viewpoint
José G.
Anaya
Facultad de Ciencias, Universidad Autónoma del Estado de México, Instituto
Literario No. 100, Col. Centro, C. P. 50000, Toluca, México.
author
Alfredo
Cano
Facultad de Ciencias, Universidad Autónoma del Estado de México, Instituto
Literario No. 100, Col. Centro, C. P. 50000, Toluca, México.
author
Enrique
Castañeda-Alvarado
Facultad de Ciencias, Universidad Autónoma del Estado de México, Instituto
Literario No. 100, Col. Centro, C. P. 50000, Toluca, México.
author
Marco A.
Castillo-Rubí
Facultad de Ciencias, Universidad Autónoma del Estado de México, Instituto
Literario No. 100, Col. Centro, C. P. 50000, Toluca, México.
author
text
article
2018
eng
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.
Khayyam Journal of Mathematics
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)
2423-4788
4
v.
1
no.
2018
13
27
http://www.kjm-math.org/article_53432_e889f317edc114515e2bb1d54c2de580.pdf
dx.doi.org/10.22034/kjm.2017.53432
A Subclass of Harmonic Univalent Functions Defined by Means of Differential Subordination
Serkan
Çakmak
Department of Mathematics, Faculty of Arts and Science, Uludag University, 16059, Görükle, Bursa, Turkey.
author
Sibel
Yalçın
Department of Mathematics, Faculty of Arts and Science, Uludag University, 16059, Görükle, Bursa, Turkey.
author
Şahsene
Altinkaya
Department of Mathematics, Faculty of Arts and Science, Uludag University, 16059, Görükle, Bursa, Turkey.
author
text
article
2018
eng
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.
Khayyam Journal of Mathematics
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)
2423-4788
4
v.
1
no.
2018
28
38
http://www.kjm-math.org/article_53655_37704e2531cb2f56dc09561deff132ef.pdf
dx.doi.org/10.22034/kjm.2017.53655
Ostrowski Type Fractional Integral Operators for Generalized Beta $(r,g)$-Preinvex Functions
Artion
Kashuri
Department of Mathematics, Faculty of Technical Science, University ”Ismail
Qemali”, Vlora, Albania.
author
Rozana
Liko
Department of Mathematics, Faculty of Technical Science, University ”Ismail
Qemali”, Vlora, Albania.
author
Tingsong
Du
College of Science, China Three Gorges University, 443002, Yichang, P. R.
China.
author
text
article
2018
eng
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.
Khayyam Journal of Mathematics
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)
2423-4788
4
v.
1
no.
2018
39
58
http://www.kjm-math.org/article_54680_ff16555c24403f6b3496ce50c6fd8bbf.pdf
dx.doi.org/10.22034/kjm.2017.54680
Constructing an Element of a Banach Space with Given Deviation from its Nested Subspaces
Asuman
Aksoy
Department of Mathematics, Claremont McKenna College, 850 Columbia Avenue, Claremont, CA 91711, USA.
author
Qidi
Peng
Institute of Mathematical Sciences, Claremont Graduate University, 710 N.
College Avenue, Claremont, CA 91711, USA.
author
text
article
2018
eng
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 $c\in(0,1]$ we can find $x_{c} \in X$, such that the distance $\rho(x_{c}, Y_n)$ from $x_{c}$ to $Y_n$ satisfies$$c d_n \leq \rho(x_{c},Y_n) \leq 4c d_n,~\mbox{for all $n\in\mathbb N$}.$$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 $d_n$.
Khayyam Journal of Mathematics
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)
2423-4788
4
v.
1
no.
2018
59
76
http://www.kjm-math.org/article_55158_6967a156928a4b5003d50eae0fedc911.pdf
dx.doi.org/10.22034/kjm.2018.55158
Laplacian and Signless Laplacian Spectrum of Commuting Graphs of Finite Groups
Jutirekha
Dutta
Department of Mathematical Sciences, Tezpur University, Napaam-784028,
Sonitpur, Assam, India.
author
Rajat
Nath
Department of Mathematical Sciences, Tezpur University, Napaam-784028,
Sonitpur, Assam, India.
author
text
article
2018
eng
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 $G\setminus Z(G)$, 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.
Khayyam Journal of Mathematics
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)
2423-4788
4
v.
1
no.
2018
77
87
http://www.kjm-math.org/article_57490_293c3a034fe521dab3aecbbd7b850f8f.pdf
dx.doi.org/10.22034/kjm.2018.57490
Polynomial Bounds for a Class of Univalent Function Involving Sigmoid Function
Olubunmi
Fadipe-Joseph
Department of Mathematics, University of Ilorin, P.M.B. 1515 Ilorin,
Nigeria.
author
Bilikis
Kadir
Department of Mathematics, University of Ilorin, P.M.B. 1515 Ilorin,
Nigeria.
author
Sunday
Akinwumi
Department of Mathematics, University of Ilorin, P.M.B. 1515 Ilorin,
Nigeria.
author
Esther
Adeniran
Department of Mathematics, University of Ilorin, P.M.B. 1515 Ilorin,
Nigeria.
author
text
article
2018
eng
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.
Khayyam Journal of Mathematics
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)
2423-4788
4
v.
1
no.
2018
88
101
http://www.kjm-math.org/article_57721_db05732ca68e42ed7238c4b1cd3b3338.pdf
dx.doi.org/10.22034/kjm.2018.57721
Ricci Solitons on Kenmotsu Manifolds under $D$-Homothetic Deformation
Halammanavar
Nagaraja
Department of Mathematics, Jnanabharathi Campus, Bangalore University,
Bengaluru, 560 056, INDIA.
author
Devasandra
Kiran Kumar
Department of Mathematics, Jnanabharathi Campus, Bangalore University,
Bengaluru, 560 056, INDIA.
author
Venkateshmurthy
Prasad
Department of Mathematics, Regional institute of Education (NCERT), Manasagangotri, Mysore, 570006, INDIA.
author
text
article
2018
eng
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.
Khayyam Journal of Mathematics
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)
2423-4788
4
v.
1
no.
2018
102
109
http://www.kjm-math.org/article_57725_899a6e6b876f185709cce8565826c41a.pdf
dx.doi.org/10.22034/kjm.2018.57725