2021-04-13T11:01:28Z
http://www.kjm-math.org/?_action=export&rf=summon&issue=12050
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
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
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
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
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
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
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
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
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
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
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
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