Khayyam Journal of MathematicsKhayyam Journal of Mathematics
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Sun, 16 Jun 2019 11:17:55 +0100FeedCreatorKhayyam Journal of Mathematics
http://www.kjm-math.org/
Feed provided by Khayyam Journal of Mathematics. Click to visit.Certain Results on Starlike and Close-to-Convex Functions
http://www.kjm-math.org/article_84141_0.html
Using the technique of differential subordination, we here, obtain certain sufficient conditions for starlike and close-to-convex functions. In most of the results obtained here, the region of variability of the differential operators implying starlikeness and close-to-convexity of analytic functions has been extended. The extended regions of the operators have been shown pictorially.Wed, 06 Mar 2019 20:30:00 +0100On a Classification of Almost $\alpha $-Cosymplectic Manifolds
http://www.kjm-math.org/article_67030_8600.html
The object of the present paper is to study almost $alpha $-cosymplectic manifolds. We consider projectively flat, conformally flat, and concircularly flat almost $alpha $-cosymplectic manifolds (with the $eta $-parallel tensor field $phi h$) and get some new properties. We conclude the paper by giving an example of $alpha $-Kenmotsu manifold, which verifies our results.Mon, 31 Dec 2018 20:30:00 +0100Power Inequalities for the Numerical Radius of Operators in Hilbert Spaces
http://www.kjm-math.org/article_84204_0.html
We generalize several inequalities involving powers of the numerical radius for the product of two operators acting on a Hilbert space. Moreover, we give a Jensen operator inequality for strongly convex functions. As a corollary, we improve the operator Hölder-McCarthy inequality under suitable conditions. In particular, we prove that if $f:Jrightarrow mathbb{R}$ is strongly convex with modulus $c$ and differentiable on ${rm int}(J)$ whose derivative is continuous on ${rm int}(J)$ and if $T$ is a self-adjoint operator on the Hilbert space $cal{H}$ with $sigma(T)subset {rm int}(J)$, then $$langle T^2x,xrangle-langle Tx,xrangle^2leq dfrac{1}{2c}(langle f'(T)Tx,xrangle -langle Tx,xrangle langle f'(T)x,xrangle)$$ for each $xincal{H}$, with $|x|=1$.Thu, 07 Mar 2019 20:30:00 +0100On General $( \alpha, \beta)$-Metrics with Some Curvature Properties
http://www.kjm-math.org/article_84205_0.html
In this paper, we study a class of Finsler metric called general $(alpha, beta)$ metrics and obtain an equation that characterizes these Finsler metrics of almost vanishing H-curvature. As a consequence of this result, we prove that a general $(alpha, beta)$-metric has almost vanishing $H$-curvature if and only if it has almost vanishing $Xi$-curvature.Thu, 07 Mar 2019 20:30:00 +0100Exponential Stability Analysis for Delay-Differential Systems of Neutral Type with an LMI Approach
http://www.kjm-math.org/article_73499_8600.html
In this paper for neutral delay differential systems, the problem of determining the exponential stability is investigated. Based on the Lyapunov method, we present some useful criteria of exponential stability for the derived systems. The stability criterion is formulated in terms of linear matrix inequality (LMI),which can be easily solved by using the MATLAB LMI toolbox. Numerical examples are included to illustrate the proposed method.Mon, 31 Dec 2018 20:30:00 +0100Traces of Schur and Kronecker Products for Block Matrices
http://www.kjm-math.org/article_84207_0.html
In this paper, we define two new Schur and Kronecker-type products for block matrices. We present some equalities and inequalities involving traces of matrices generated by these products and in particular we give conditions under which the trace operator is sub-multiplicative for them. Also, versions in the block matrix framework of results of Das, Vashisht, Taskara and Gumus will be obtained.Thu, 07 Mar 2019 20:30:00 +0100The Approximate Solutions of Fractional Integro-Differential Equations by Using Modified ...
http://www.kjm-math.org/article_73593_8600.html
The main object of the present paper is to study the behavior of the approximated solutions of the Caputo fractional Volterra-Fredholm integro-differential equations by using modified Adomian decomposition method. Moreover, we discuss some new existence, uniqueness, and convergence results. Finally, an example is included to demonstrate the validity and applicability of the proposed technique.Mon, 31 Dec 2018 20:30:00 +0100Direct Estimates for Stancu Variant of Lupaş-Durrmeyer Operators Based On Polya Distribution
http://www.kjm-math.org/article_85886_0.html
In this paper, we study approximation properties of a family of linear positive operators and establish the Voronovskaja type asymptotic formula, local approximation and pointwise estimates using the Lipschitz type maximal function. In the last section, we consider the King type modification of these operators to obtain better estimates.Tue, 09 Apr 2019 19:30:00 +0100Dynamic Response of an Elastically Connected Double Non-Mindlin Plates with Simply-Supported ...
http://www.kjm-math.org/article_73854_8600.html
In this paper, the dynamic response of two identical parallel non-mindlin (i.e., not taking into account the effect of shear deformation and rotatory inertia) plates which are elastically connected and subjected to a constant moving load is considered. The fourth order coupled partial differential governing equations is formulated and solved, using an approximate analytical method by assuming; firstly, a series solution later on treating the resulting coupled second order ordinary differential equations with an asymptotic method of Struble. The differential transform method, being a semi-analytical technique, is applied to the reduced coupled second order ordinary differential equations, to get a non-oscillatory series solution. An after treatment technique, comprising of the Laplace transform and Pade approximation techniques, is finally used via MAPLE ODE solver to make the series solution oscillatory. The dynamic deflections of the upper and lower plates are presented in analytical closed forms. The effect of the moving speed of the load and the elasticity of the elastic layer on the dynamic responses of the double plate systems is graphically shown and studied in details. The graphs of the plate's deflections for different speed parameters were plotted. It is however observed that the transverse deflections of each of the plates increase with an increase in different values of velocities for the moving load for a fixed time $t$.Mon, 31 Dec 2018 20:30:00 +0100Slant Toeplitz Operators on the Lebesgue Space of the Torus
http://www.kjm-math.org/article_86133_0.html
This paper introduces the class of slant Toeplitz operators on the Lebesgue space of the torus. A characterization of these operators as the solutions of an operator equation is obtained. The paper describes various algebraic properties of these operators. The compactness, commutativity and essential commutativity of these operators are also discussed.Thu, 18 Apr 2019 19:30:00 +0100On T-Extensions of Abelian Groups
http://www.kjm-math.org/article_74220_8600.html
Let $Re$ be the category of all discrete abelian groups, and let $cal{L}$ be the category of all locally compact abelian (LCA) groups. For a group $Gin cal{L}$, the maximal torsion subgroup of $G$ is denoted by $tG$. A short exact sequence $0to Astackrel{phi}{to} Bstackrel{psi}{to}Cto 0$ in $Re$ is said to be a t-extension if $0to tAstackrel{phi}{to} tBstackrel{psi}{to}tCto 0$ is a short exact sequence. We show that the set of all t-extensions of $A$ by $C$ is a subgroup of $Ext(C,A)$, which contains $Pext(C,A)$ for discrete abelian groups $A$ and $C$. We establish conditions under which the t-extensions split and determine those groups in $Re$ which are t-injective or t-projective in $Re$. Finally we determine the compact groups $G$ in $cal{L}$ such that every pure extension of $G$ by a compact connected group $Cin cal{L}$ splits.Mon, 31 Dec 2018 20:30:00 +0100Conformal Semi-Invariant Submersions from Almost Contact Metric Manifolds onto Riemannian Manifolds
http://www.kjm-math.org/article_88074_0.html
As a generalization of semi-invariant Riemannian submersions, we introduce conformal semi-invariant submersions from almost contact metric manifolds onto Riemannian manifolds and study such submersions from Cosymplectic manifolds onto Riemannian manifolds. Examples of conformal semi-invariant submersions in which structure vector field is vertical are given. We study geometry of foliations determined by distributions involved in definition of conformal anti-invariant submersions. We also study the harmonicity of such submersions and find necessary and sufficient conditions for the distributions to be totally geodesic.Sun, 26 May 2019 19:30:00 +0100On Randers Change of Generalized $m$th Root Metric
http://www.kjm-math.org/article_75278_8600.html
In the present paper, we find a condition under which a Finsler space with Randers change of generalized $m$th root metric is projectively related to an $m$th root metric. Then we find a condition under which Randers change of generalized $m$th root Finsler metric is locally projectively flat and also find a condition for locally dually flatness.Mon, 31 Dec 2018 20:30:00 +0100Local Convergence of a Novel Eighth Order Method under Hypotheses Only on the First Derivative
http://www.kjm-math.org/article_88082_0.html
We expand the applicability of eighth order-iterative method studied by Jaiswal in order to approximate a locally unique solution of an equation in Banach space setting. We provide a local convergence analysis using only hypotheses on the first Frechet-derivative. Moreover, we provide computable convergence radii, error bounds, and uniqueness results. Numerical examples computing the radii of the convergence balls as well as examples where earlier results cannot apply to solve equations but our results can apply are also given in this study.Sun, 26 May 2019 19:30:00 +0100Ruscheweyh-Type Harmonic Functions Defined By $q$- Differential Operators
http://www.kjm-math.org/article_81212_8600.html
A class of Ruscheweyh-type harmonic functions is defined, using $q$-differential operators and sufficient coefficient conditions for this class is determined. We then consider a subclass of the aforementioned class consisting of functions with real coefficients and obtain necessary and sufficient coefficient bounds, distortion theorem, extreme points, and convex combination conditions for such class. It is shown that the classes of functions considered in this paper contain various well-known as well as new classes of harmonic functions.Mon, 31 Dec 2018 20:30:00 +0100On Certain Conditions for Convex Optimization in Hilbert Spaces
http://www.kjm-math.org/article_88084_0.html
In this paper convex optimization techniques are employed for convex optimization problems in infinite dimensional Hilbert spaces. A first order optimality condition is given. Let $f : mathbb{R}^{n}rightarrow mathbb{R}$ and let $xin mathbb{R}^{n}$ be a local solution to the problem $min_{xin mathbb{R}^{n}} f(x).$ Then $f'(x,d)geq 0$ for every direction $din mathbb{R}^{n}$ for which $f'(x,d)$ exists. Moreover, Let $f : mathbb{R}^{n}rightarrow mathbb{R}$ be differentiable at $x^{*}in mathbb{R}^{n}.$ If $x^{*}$ is a local minimum of $f$, then $nabla f(x^{*}) = 0.$ A simple application involving the Dirichlet problem is also given.Sun, 26 May 2019 19:30:00 +0100Almost conformal Ricci solitons on $f$-Kenmotsu Manifolds
http://www.kjm-math.org/article_81221_8600.html
The object of the present paper is to study the $phi $-Ricci symmetric, locally $phi $-Ricci symmetric and cyclic Ricci parallel three-dimensional $f$-Kenmotsu manifold bearing the function $f$ being constant. We have considered almost conformal Ricci soliton on the three-dimensional $f$-Kenmostu manifold and deduced the condition for an almost conformal Ricci soliton, which becomes conformal Ricci soliton. Finally, examples on three-dimensional $f$-Kenmotsu manifold depending on nature of $f$ are constructed to illustrate the results.Mon, 31 Dec 2018 20:30:00 +0100Proximal Point Algorithms for Finding Common Fixed Points of a Finite Family of Nonexpansive ...
http://www.kjm-math.org/article_88426_0.html
We start by showing that the composition of fixed point of minimization problem and a finite family of multivalued nonexpansive mapping are equal to the common solution of the fixed point of each of the aforementioned problems, that is, $F(J_{lambda}^fcirc T_i) = F(J_{lambda}^f)cap F(T_i)=Gamma.$ Furthermore, we then propose an iterative algorithm and prove weak and strong convergence results for approximating the common solution of the minimization problem and fixed point problem of a multivalued nonexpansive mapping in the framework of real Hilbert space. Our result extends and complements some related results in literature.Wed, 05 Jun 2019 19:30:00 +0100On The Stability of The Quasi-Linear Implicit Equations in Hilbert Spaces
http://www.kjm-math.org/article_81222_8600.html
We use the generalized theorem of Liapounov to obtain some necessary and sufficient conditions for the stability of the stationary implicit equation $$Ax'(t)=Bx(t) ,quad tgeq 0 ,$$ where $A$ and $B$ are bounded operators in Hilbert spaces. The achieved results can be applied to the stability for the quasi-linear implicit equation $$Ax'(t)=Bx(t)+theta(t,x(t)),quad tgeq 0 .$$Mon, 31 Dec 2018 20:30:00 +0100On Starlikeness, Convexity, and Close-to-Convexity of Hyper-Bessel Function
http://www.kjm-math.org/article_88427_0.html
In the present investigation, our main aim is to derive some conditions on starlikeness, convexity, and close-to-convexity of normalized hyper-Bessel functions. Also we give some similar results for classical Bessel functions by using the relationships between hyper-Bessel and Bessel functions. As a result of the obtained conditions, some examples are also given.Wed, 05 Jun 2019 19:30:00 +0100On Approximation by $(p,q)$-Meyer-König-Zeller Durrmeyer Operators
http://www.kjm-math.org/article_81223_8600.html
In this paper, we introduce a Durrmeyer type modification of Meyer-König-Zeller operators based on $(p,q)$-integers. The rate of convergence of these operators is explored with the help of Korovkin type theorems. We establish some direct results for proposed operators. We also obtain statistical approximation properties of operators. In the last section, we show the rate of convergence of $(p,q)$-Meyer-König-Zeller Durrmeyer operators for some functions by means of MATLAB programming.Mon, 31 Dec 2018 20:30:00 +0100Convergence of Operators with Closed Range
http://www.kjm-math.org/article_88428_0.html
Izumino has discussed a sequence of closed range operators $(T_n)$ that converges to a closed range operator $T$ on a Hilbert space to establish the convergence of $T^{dag}_n$ $to$ $T^{dag}$ for Moore-Penrose inverses. In general, if $T_n to T$ uniformly and each $T_n$ has a closed range, then $T$ need not have a closed range. Some sufficient conditions have been discussed on $T_n$ and $T$ such that $T$ has a closed range whenever each $T_n$ has a closed range.Wed, 05 Jun 2019 19:30:00 +0100On Two Generation Methods for The Simple Linear Group $PSL(3,5)$
http://www.kjm-math.org/article_81226_8600.html
A finite group $G$ is said to be $(l,m, n)$-generated, if it is a quotient group of the triangle group $T(l,m, n) = left<x,y, z|x^{l} = y^{m} = z^{n} = xyz = 1right>.$ In [Nova J. Algebra and Geometry, 2 (1993), no. 3, 277--285], Moori posed the question of finding all the $(p,q,r)$ triples, where $p, q,$ and $r$ are prime numbers, such that a nonabelian finite simple group $G$ is $(p,q,r)$-generated. Also for a finite simple group $G$ and a conjugacy class $X$ of $G,$ the rank of $X$ in $G$ is defined to be the minimal number of elements of $X$ generating $G.$ In this paper, we investigate these two generational problems for the group $PSL(3,5),$ where we will determine the $(p,q,r)$-generations and the ranks of the classes of $PSL(3,5).$ We approach these kind of generations using the structure constant method. GAP [The GAP Group, GAP-Groups, Algorithms, and Programming, Version 4.9.3; 2018. (http://www.gap-system.org)] is used in our computations.Mon, 31 Dec 2018 20:30:00 +0100Coefficients of Bi-Univalent Functions Involving Pseudo-Starlikeness Associated with Chebyshev ...
http://www.kjm-math.org/article_81231_8600.html
In the present paper, a new subclass of analytic and bi-univalent functions by means of pseudo starlike function, activation function and Chebyshev polynomials are introduced. Coefficient bounds for functions belonging to the said subclass are obtained. Relevance connection of our class to second Hankel determinants is established.Mon, 31 Dec 2018 20:30:00 +0100