Khayyam Journal of MathematicsKhayyam Journal of Mathematics
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Feed provided by Khayyam Journal of Mathematics. Click to visit.Local Convergence for a Family of Sixth Order Chebyshev-Halley-Type Methods in Banach Space ...
http://www.kjm-math.org/article_51873_7187.html
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.Sun, 31 Dec 2017 20:30:00 +0100The Second Symmetric Product of Finite Graphs from a Homotopical Viewpoint
http://www.kjm-math.org/article_53432_7187.html
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.Sun, 31 Dec 2017 20:30:00 +0100A Subclass of Harmonic Univalent Functions Defined by Means of Differential Subordination
http://www.kjm-math.org/article_53655_7187.html
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.Sun, 31 Dec 2017 20:30:00 +0100Ostrowski Type Fractional Integral Operators for Generalized Beta $(r,g)$-Preinvex Functions
http://www.kjm-math.org/article_54680_7187.html
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.Sun, 31 Dec 2017 20:30:00 +0100Constructing an Element of a Banach Space with Given Deviation from its Nested Subspaces
http://www.kjm-math.org/article_55158_7187.html
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 $d_n$.Sun, 31 Dec 2017 20:30:00 +0100Laplacian and Signless Laplacian Spectrum of Commuting Graphs of Finite Groups
http://www.kjm-math.org/article_57490_7187.html
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.Sun, 31 Dec 2017 20:30:00 +0100Polynomial Bounds for a Class of Univalent Function Involving Sigmoid Function
http://www.kjm-math.org/article_57721_7187.html
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.Sun, 31 Dec 2017 20:30:00 +0100Ricci Solitons on Kenmotsu Manifolds under $D$-Homothetic Deformation
http://www.kjm-math.org/article_57725_7187.html
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.Sun, 31 Dec 2017 20:30:00 +0100