Khayyam Journal of MathematicsKhayyam Journal of Mathematics
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Sat, 23 Jun 2018 11:00:46 +0100FeedCreatorKhayyam 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 +0100Accurate Numerical Method for Singularly Perturbed Differential-Difference Equations with Mixed ...
http://www.kjm-math.org/article_57949_0.html
This paper is concerned with the numerical solution of the singularly perturbed differential-difference equations with small shifts called delay and advanced parameters. A fourth order finite difference method with a fitting factor is proposed for the solution of the singularly perturbed differential-difference equations with mixed shifts. The delay and advanced shifts are managed by Taylor series and an asymptotically equivalent singularly perturbed two-point boundary value problem is obtained. A fitting factor is introduced in the fourth order finite difference scheme for the problem which takes care of the small values of the perturbation parameter. This fitting factor is obtained from the asymptotic solution of singular perturbations. Thomas algorithm is used to solve the discrete system of the difference scheme. Convergence of the proposed method is analyzed. Maximum absolute errors in comparison with the several numerical experiments aretabulated to illustrate the proposed method.Thu, 22 Feb 2018 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 +0100On Certain Results Involving a Multiplier Transformation in a Parabolic Region
http://www.kjm-math.org/article_60177_0.html
We, here, obtain certain results in subordination form involving a multiplier transformation in a parabolic region. In particular, using different dominants in our main result, we derive certain results on parabolic starlikeness, starlikeness, convexity, uniform convexity, strongly starlikeness, close-to-convexity and uniform close-to-convexity of p-valent analytic functions as well as univalent analytic functions.Tue, 03 Apr 2018 19:30:00 +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 +0100More on Convergence Theory of Proper Multisplittings
http://www.kjm-math.org/article_60178_0.html
In this paper, we first prove a few comparison results between twoproper weak regular splittings which are useful in getting theiterative solution of a large class of rectangular (square singular)linear system of equations $Ax = b$, in a faster way. We then deriveconvergence and comparison results for proper weak regularmultisplittings.Tue, 03 Apr 2018 19:30:00 +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 +0100Uniqueness of Meromorphic Functions with Regard to Multiplicity
http://www.kjm-math.org/article_60179_0.html
In this paper, we investigate the uniqueness problem on meromorphic functions concerning differential polynomials sharing one value. A uniqueness result which related to multiplicity of meromorphic function is proved in this paper. By using the notion of multilplicity our results will generalise and improve the result due to Chao Meng [10].Tue, 03 Apr 2018 19:30:00 +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 +0100Expanding the Applicability of Generalized High Convergence Order Methods for Solving Equations
http://www.kjm-math.org/article_63368_0.html
The local convergence analysis of iterative methods is important since it indicates the degree of difficulty for choosing initial points. In the present study we introduce generalized three step high order methods for solving nonlinear equations. The local convergence analysis is given using hypotheses only on the first derivative, which actually appears in the methods in contrast to earlier works using hypotheses on higher derivatives. This way we extend the applicability of these methods. The analysis includes computable radius of convergence as well as error bounds based on Lipschitz-type conditions, which is not given in earlier studies. Numerical examples conclude this study.Sun, 03 Jun 2018 19:30:00 +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 +0100Generalized Ricci Solitons on Trans-Sasakian Manifolds
http://www.kjm-math.org/article_63446_0.html
The object of the present research is to shows that a trans-Sasakian manifold, which also satisfies the Ricci soliton and generalized Ricci soliton equation, satisfying some conditions, is necessarily the Einstein manifold.Tue, 05 Jun 2018 19:30:00 +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 +0100On a New Subclass of m-Fold Symmetric Biunivalent Functions Equipped with Subordinate Conditions
http://www.kjm-math.org/article_63470_0.html
In this paper, we introduce a new subclass of biunivalent function class $Sigma$ in which both $f(z)$ and $f^{-1}(z)$ are m-fold symmetric analytic functions. For functions of the subclass introduced in this paper, we obtain the coefficient bounds for $|a_{m+1}|$ and $|a_{2m+1}|$ and also study the Fekete-Szegö functional estimate for this class. Consequences of the results are also discussed.Thu, 07 Jun 2018 19:30:00 +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