Khayyam Journal of MathematicsKhayyam Journal of Mathematics
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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_8600.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.Sun, 30 Jun 2019 19:30:00 +0100Power Inequalities for the Numerical Radius of Operators in Hilbert Spaces
http://www.kjm-math.org/article_84204_8600.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 $|x|=1$.Sun, 30 Jun 2019 19:30:00 +0100On General $( \alpha, \beta)$-Metrics with Some Curvature Properties
http://www.kjm-math.org/article_84205_8600.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.Sun, 30 Jun 2019 19:30:00 +0100Traces of Schur and Kronecker Products for Block Matrices
http://www.kjm-math.org/article_84207_8600.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.Sun, 30 Jun 2019 19:30:00 +0100Direct Estimates for Stancu Variant of Lupaş-Durrmeyer Operators Based On Polya Distribution
http://www.kjm-math.org/article_85886_8600.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.Sun, 30 Jun 2019 19:30:00 +0100Slant Toeplitz Operators on the Lebesgue Space of the Torus
http://www.kjm-math.org/article_86133_8600.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.Sun, 30 Jun 2019 19:30:00 +0100Conformal Semi-Invariant Submersions from Almost Contact Metric Manifolds onto Riemannian Manifolds
http://www.kjm-math.org/article_88074_8600.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, 30 Jun 2019 19:30:00 +0100Local Convergence of a Novel Eighth Order Method under Hypotheses Only on the First Derivative
http://www.kjm-math.org/article_88082_8600.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, 30 Jun 2019 19:30:00 +0100On Certain Conditions for Convex Optimization in Hilbert Spaces
http://www.kjm-math.org/article_88084_8600.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, 30 Jun 2019 19:30:00 +0100Proximal Point Algorithms for Finding Common Fixed Points of a Finite Family of Nonexpansive ...
http://www.kjm-math.org/article_88426_8600.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.Sun, 30 Jun 2019 19:30:00 +0100On Starlikeness, Convexity, and Close-to-Convexity of Hyper-Bessel Function
http://www.kjm-math.org/article_88427_8600.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.Sun, 30 Jun 2019 19:30:00 +0100Convergence of Operators with Closed Range
http://www.kjm-math.org/article_88428_8600.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.Sun, 30 Jun 2019 19:30:00 +0100