Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
Khayyam Journal of Mathematics
2423-4788
5
2
2019
07
01
Certain Results on Starlike and Close-to-Convex Functions
1
14
EN
Pardeep
Kaur
Department of Applied Sciences, Baba Banda Singh Bahadur Engineering
College, Fatehgarh Sahib-140407, Punjab, India.
aradhitadhiman@gmail.com
Sukhwinder
Singh
Billing
Department of Mathematics, Sri Guru Granth Shaib World University, Fatehgarh Sahib-140407, Punjab, India.
ssbilling@gmail.com
10.22034/kjm.2019.84141
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
http://www.kjm-math.org/article_84141.html
http://www.kjm-math.org/article_84141_ae4b8ee0e542e44c6a493733d70415a8.pdf
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
Khayyam Journal of Mathematics
2423-4788
5
2
2019
07
01
Power Inequalities for the Numerical Radius of Operators in Hilbert Spaces
15
29
EN
Mohammad
H.M.
Rashid
Department of Mathematics and Statistics, Faculty of Science P.O.Box(7),
Mu’tah University, Alkarak-Jordan.
malik_okasha@yahoo.com
10.22034/kjm.2019.84204
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 <span>Hölder-McCarthy</span> 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<br /> $$langle T^2x,xrangle-langle Tx,xrangle^2leq dfrac{1}{2c}(langle f'(T)Tx,xrangle -langle Tx,xrangle langle f'(T)x,xrangle)$$<br /> for each $xincal{H}$, with $|x|=1$.
Numerical Range,Numerical radius,Aluthge transformation,strongly convex
http://www.kjm-math.org/article_84204.html
http://www.kjm-math.org/article_84204_a321253ff5f81d65f8472735f8eb5f80.pdf
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
Khayyam Journal of Mathematics
2423-4788
5
2
2019
07
01
On General $( alpha, beta)$-Metrics with Some Curvature Properties
30
39
EN
Bankteshwar
Tiwari
DST-CIMS, Institute of Science, Banaras Hindu University, Varanasi-221005,
India.
banktesht@gmail.com
Ranadip
Gangopadhyay
0000-0003-0989-3143
DST-CIMS, Institute of Science, Banaras Hindu University, Varanasi-221005,
India.
gangulyranadip@gmail.com
Ghanashyam
Kr.
Prajapati
Loknayak Jai Prakash Institute of Technology, Chhapra-841302, India.
gspbhu@gmail.com
10.22034/kjm.2019.84205
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
http://www.kjm-math.org/article_84205.html
http://www.kjm-math.org/article_84205_7a50131e4fbba322eb53ea4697d49b67.pdf
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
Khayyam Journal of Mathematics
2423-4788
5
2
2019
07
01
Traces of Schur and Kronecker Products for Block Matrices
40
50
EN
Ismael
García-Bayona
0000-0003-1027-5086
Departamento de Análisis Matemático, Universidad de Valencia, 46100 Burjassot, Valencia, Spain.
garbais@uv.es
10.22034/kjm.2019.84207
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
http://www.kjm-math.org/article_84207.html
http://www.kjm-math.org/article_84207_18a097d3d32ba04b3cab1968f04ce4ff.pdf
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
Khayyam Journal of Mathematics
2423-4788
5
2
2019
07
01
Direct Estimates for Stancu Variant of Lupaş-Durrmeyer Operators Based On Polya Distribution
51
64
EN
Lakshmi
Narayan
Mishra
0000-0001-7774-7290
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT) University, Vellore 632 014, Tamil Nadu, India.
lakshminarayanmishra04@gmail.com
Alok
Kumar
0000-0002-5171-1393
Department of Computer Science, Dev Sanskriti Vishwavidyalaya, Haridwar-
249411, Uttarakhand, India.
alokkpma@gmail.com
10.22034/kjm.2019.85886
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
http://www.kjm-math.org/article_85886.html
http://www.kjm-math.org/article_85886_29d744acfffe5c453538e24c39189d1b.pdf
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
Khayyam Journal of Mathematics
2423-4788
5
2
2019
07
01
Slant Toeplitz Operators on the Lebesgue Space of the Torus
65
76
EN
Gopal
Datt
Department of Mathematics, PGDAV College, University of Delhi, Delhi-110065 (INDIA).
gopal.d.sati@gmail.com
Neelima
Ohri
Department of Mathematics, University of Delhi, Delhi - 110007 (INDIA).
neelimaohri1990@gmail.com
10.22034/kjm.2019.86133
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
http://www.kjm-math.org/article_86133.html
http://www.kjm-math.org/article_86133_d0ddc2ce6b15b61ebf8dd33d6d518696.pdf
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
Khayyam Journal of Mathematics
2423-4788
5
2
2019
07
01
Conformal Semi-Invariant Submersions from Almost Contact Metric Manifolds onto Riemannian Manifolds
77
95
EN
Rajendra
Prasad
Department of mathematics and Astronomy, University of Lucknow, Lucknow, India
rp.manpur@rediffmail.com
Sushil
Kumar
Department of mathematics and Astronomy, University of Lucknow, Lucknow, India
sushilmath20@gmail.com
10.22034/kjm.2018.68796
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
http://www.kjm-math.org/article_88074.html
http://www.kjm-math.org/article_88074_f69b8a26e1688c8808176fbc7ab43cde.pdf
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
Khayyam Journal of Mathematics
2423-4788
5
2
2019
07
01
Local Convergence of a Novel Eighth Order Method under Hypotheses Only on the First Derivative
96
107
EN
Ioannis
K.
Argyros
0000-0002-9189-9298
Department of Mathematical Sciences, Cameron University, Lawton, OK
73505, USA
iargyros@cameron.edu
Santhosh
George
0000-0002-3530-5539
Department of Mathematical and Computational Sciences, NIT Karnataka,
575 025, India
sgeorge@nitk.edu.in
Shobha
M.
Erappa
Department of Mathematics, Manipal Institute of Technology, Manipal,
Karnataka, 576104, India
shobha.me@gmail.com
10.22034/kjm.2019.88082
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
http://www.kjm-math.org/article_88082.html
http://www.kjm-math.org/article_88082_705a0abeb572a4da9c9b55a24aaf5217.pdf
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
Khayyam Journal of Mathematics
2423-4788
5
2
2019
07
01
On Certain Conditions for Convex Optimization in Hilbert Spaces
108
112
EN
Benard
Okelo
0000 0001 2345 6789
Department of Pure and Applied Mathematics, School of Mathematics and
Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology, Box 210-40601, Bondo-Kenya.
bnyaare@yahoo.com
10.22034/kjm.2019.88084
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.
Optimization problem,convex function,Hilbert space
http://www.kjm-math.org/article_88084.html
http://www.kjm-math.org/article_88084_b5eebff35178eb5f92b22a462b6c4f8b.pdf
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
Khayyam Journal of Mathematics
2423-4788
5
2
2019
07
01
Proximal Point Algorithms for Finding Common Fixed Points of a Finite Family of Nonexpansive Multivalued Mappings in Real Hilbert Spaces
113
123
EN
Akindele
Adebayo
Mebawondu
School of Mathematics, Statistics and Computer Science, University of KwaZuluNatal, Durban, South Africa
dele@aims.ac.za
10.22034/kjm.2019.88426
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.
Proximal point algorithms,fixed point,multivalued nonexpansive mapping,Hilbert space
http://www.kjm-math.org/article_88426.html
http://www.kjm-math.org/article_88426_f7ea9c7dc575d3815a88a6312c349e52.pdf
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
Khayyam Journal of Mathematics
2423-4788
5
2
2019
07
01
On Starlikeness, Convexity, and Close-to-Convexity of Hyper-Bessel Function
124
131
EN
İbrahim
Aktaş
0000-0003-4570-4485
Department of Mathematics, Kamil Özdağ Science Faculty, Karamanoğlu Mehmetbey Uninersity, Karaman, Turkey.
aktasibrahim38@gmail.com
10.22034/kjm.2019.88427
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
http://www.kjm-math.org/article_88427.html
http://www.kjm-math.org/article_88427_8d40602648d983ede04029651f1117c4.pdf
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
Khayyam Journal of Mathematics
2423-4788
5
2
2019
07
01
Convergence of Operators with Closed Range
132
138
EN
P.
Sam
Johnson
0000-0003-3461-5380
Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Surathkal, Karnataka - 575 025, India.
nitksam@gmail.com
S.
Balaji
Department of Mathematics, School of Advanced Sciences, Vellore Institute
of Technology, Vellore, Tamilnadu - 632 014, India.
balajimath@gmail.com
10.22034/kjm.2019.88428
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
http://www.kjm-math.org/article_88428.html
http://www.kjm-math.org/article_88428_0bd9bda9f59db84efd3662be88f82bc7.pdf