2021-04-13T11:01:28Z http://www.kjm-math.org/?_action=export&rf=summon&issue=12050
2019-07-01 10.22034
Khayyam Journal of Mathematics Khayyam J. Math. 2019 5 2 Certain Results on Starlike and Close-to-Convex Functions Pardeep Kaur Sukhwinder Billing 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. starlike function close-to-convex function Bazilevič function differential subordination 2019 07 01 1 14 http://www.kjm-math.org/article_84141_ae4b8ee0e542e44c6a493733d70415a8.pdf
2019-07-01 10.22034
Khayyam Journal of Mathematics Khayyam J. Math. 2019 5 2 Power Inequalities for the Numerical Radius of Operators in Hilbert Spaces Mohammad Rashid 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 $f:J\rightarrow \mathbb{R}$ 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 $$\langle T^2x,x\rangle-\langle Tx,x\rangle^2\leq \dfrac{1}{2c}(\langle f'(T)Tx,x\rangle -\langle Tx,x\rangle \langle f'(T)x,x\rangle)$$ for each $x\in\cal{H}$, with $\|x\|=1$. Numerical Range Numerical radius Aluthge transformation strongly convex 2019 07 01 15 29 http://www.kjm-math.org/article_84204_a321253ff5f81d65f8472735f8eb5f80.pdf
2019-07-01 10.22034
Khayyam Journal of Mathematics Khayyam J. Math. 2019 5 2 On General $( alpha, beta)$-Metrics with Some Curvature Properties Bankteshwar Tiwari Ranadip Gangopadhyay Ghanashyam Prajapati 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. Finsler space General (α, β)-metric Ξ-curvature $H$-curvature 2019 07 01 30 39 http://www.kjm-math.org/article_84205_7a50131e4fbba322eb53ea4697d49b67.pdf
2019-07-01 10.22034
Khayyam Journal of Mathematics Khayyam J. Math. 2019 5 2 Traces of Schur and Kronecker Products for Block Matrices Ismael García-Bayona 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. Schur product Kronecker product Trace matrix multiplication inequalities 2019 07 01 40 50 http://www.kjm-math.org/article_84207_18a097d3d32ba04b3cab1968f04ce4ff.pdf
2019-07-01 10.22034
Khayyam Journal of Mathematics Khayyam J. Math. 2019 5 2 Direct Estimates for Stancu Variant of Lupaş-Durrmeyer Operators Based On Polya Distribution Lakshmi Mishra Alok Kumar 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. Asymptotic formula Modulus of continuity $K$-functional Polya distribution local approximation 2019 07 01 51 64 http://www.kjm-math.org/article_85886_29d744acfffe5c453538e24c39189d1b.pdf
2019-07-01 10.22034
Khayyam Journal of Mathematics Khayyam J. Math. 2019 5 2 Slant Toeplitz Operators on the Lebesgue Space of the Torus Gopal Datt Neelima Ohri 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. Toeplitz operator slant Toeplitz operator bidisk Torus 2019 07 01 65 76 http://www.kjm-math.org/article_86133_d0ddc2ce6b15b61ebf8dd33d6d518696.pdf
2019-07-01 10.22034
Khayyam Journal of Mathematics Khayyam J. Math. 2019 5 2 Conformal Semi-Invariant Submersions from Almost Contact Metric Manifolds onto Riemannian Manifolds Rajendra Prasad Sushil Kumar 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. Riemannian submersion anti-invariant submersion conformal semi-invariant submersions 2019 07 01 77 95 http://www.kjm-math.org/article_88074_f69b8a26e1688c8808176fbc7ab43cde.pdf
2019-07-01 10.22034
Khayyam Journal of Mathematics Khayyam J. Math. 2019 5 2 Local Convergence of a Novel Eighth Order Method under Hypotheses Only on the First Derivative Ioannis Argyros Santhosh George Shobha Erappa 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. Eighth order of convergence ball convergence Banach space Frechet-derivative 2019 07 01 96 107 http://www.kjm-math.org/article_88082_705a0abeb572a4da9c9b55a24aaf5217.pdf
2019-07-01 10.22034
Khayyam Journal of Mathematics Khayyam J. Math. 2019 5 2 On Certain Conditions for Convex Optimization in Hilbert Spaces Benard Okelo 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 $x\in \mathbb{R}^{n}$ be a local solution to the problem $\min_{x\in \mathbb{R}^{n}} f(x).$ Then $f'(x,d)\geq 0$ for every direction $d\in \mathbb{R}^{n}$ 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. Optimization problem convex function Hilbert space 2019 07 01 108 112 http://www.kjm-math.org/article_88084_b5eebff35178eb5f92b22a462b6c4f8b.pdf
2019-07-01 10.22034
Khayyam Journal of Mathematics Khayyam J. Math. 2019 5 2 Proximal Point Algorithms for Finding Common Fixed Points of a Finite Family of Nonexpansive Multivalued Mappings in Real Hilbert Spaces Akindele Mebawondu 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, $F(J_{\lambda}^f\circ T_i) = F(J_{\lambda}^f)\cap F(T_i)=\Gamma.$ 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. Proximal point algorithms fixed point multivalued nonexpansive mapping Hilbert space 2019 07 01 113 123 http://www.kjm-math.org/article_88426_f7ea9c7dc575d3815a88a6312c349e52.pdf
2019-07-01 10.22034
Khayyam Journal of Mathematics Khayyam J. Math. 2019 5 2 On Starlikeness, Convexity, and Close-to-Convexity of Hyper-Bessel Function İbrahim Aktaş 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. Analytic function hyper-Bessel function Starlike convex and close-to-convex functions 2019 07 01 124 131 http://www.kjm-math.org/article_88427_8d40602648d983ede04029651f1117c4.pdf
2019-07-01 10.22034
Khayyam Journal of Mathematics Khayyam J. Math. 2019 5 2 Convergence of Operators with Closed Range P. Johnson S. Balaji 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. Frechet spaces closed range operators Moore-Penrose inverses 2019 07 01 132 138 http://www.kjm-math.org/article_88428_0bd9bda9f59db84efd3662be88f82bc7.pdf