eng
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
2423-4788
2019-07-01
5
2
1
14
10.22034/kjm.2019.84141
84141
Certain Results on Starlike and Close-to-Convex Functions
Pardeep Kaur
aradhitadhiman@gmail.com
1
Sukhwinder Billing
ssbilling@gmail.com
2
Department of Applied Sciences, Baba Banda Singh Bahadur Engineering College, Fatehgarh Sahib-140407, Punjab, India.
Department of Mathematics, Sri Guru Granth Shaib World University, Fatehgarh Sahib-140407, Punjab, India.
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.
http://www.kjm-math.org/article_84141_ae4b8ee0e542e44c6a493733d70415a8.pdf
starlike function
close-to-convex function
Bazilevič function
differential subordination
eng
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
2423-4788
2019-07-01
5
2
15
29
10.22034/kjm.2019.84204
84204
Power Inequalities for the Numerical Radius of Operators in Hilbert Spaces
Mohammad Rashid
malik_okasha@yahoo.com
1
Department of Mathematics and Statistics, Faculty of Science P.O.Box(7), Mu’tah University, Alkarak-Jordan.
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 $|x|=1$.
http://www.kjm-math.org/article_84204_a321253ff5f81d65f8472735f8eb5f80.pdf
Numerical Range
Numerical radius
Aluthge transformation
strongly convex
eng
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
2423-4788
2019-07-01
5
2
30
39
10.22034/kjm.2019.84205
84205
On General $( alpha, beta)$-Metrics with Some Curvature Properties
Bankteshwar Tiwari
banktesht@gmail.com
1
Ranadip Gangopadhyay
gangulyranadip@gmail.com
2
Ghanashyam Prajapati
gspbhu@gmail.com
3
DST-CIMS, Institute of Science, Banaras Hindu University, Varanasi-221005, India.
DST-CIMS, Institute of Science, Banaras Hindu University, Varanasi-221005, India.
Loknayak Jai Prakash Institute of Technology, Chhapra-841302, India.
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.
http://www.kjm-math.org/article_84205_7a50131e4fbba322eb53ea4697d49b67.pdf
Finsler space
General (α, β)-metric
Ξ-curvature
$H$-curvature
eng
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
2423-4788
2019-07-01
5
2
40
50
10.22034/kjm.2019.84207
84207
Traces of Schur and Kronecker Products for Block Matrices
Ismael García-Bayona
garbais@uv.es
1
Departamento de Análisis Matemático, Universidad de Valencia, 46100 Burjassot, Valencia, Spain.
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.
http://www.kjm-math.org/article_84207_18a097d3d32ba04b3cab1968f04ce4ff.pdf
Schur product
Kronecker product
Trace
matrix multiplication
inequalities
eng
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
2423-4788
2019-07-01
5
2
51
64
10.22034/kjm.2019.85886
85886
Direct Estimates for Stancu Variant of Lupaş-Durrmeyer Operators Based On Polya Distribution
Lakshmi Mishra
lakshminarayanmishra04@gmail.com
1
Alok Kumar
alokkpma@gmail.com
2
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT) University, Vellore 632 014, Tamil Nadu, India.
Department of Computer Science, Dev Sanskriti Vishwavidyalaya, Haridwar- 249411, Uttarakhand, India.
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.
http://www.kjm-math.org/article_85886_29d744acfffe5c453538e24c39189d1b.pdf
Asymptotic formula
Modulus of continuity
$K$-functional
Polya distribution
local approximation
eng
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
2423-4788
2019-07-01
5
2
65
76
10.22034/kjm.2019.86133
86133
Slant Toeplitz Operators on the Lebesgue Space of the Torus
Gopal Datt
gopal.d.sati@gmail.com
1
Neelima Ohri
neelimaohri1990@gmail.com
2
Department of Mathematics, PGDAV College, University of Delhi, Delhi-110065 (INDIA).
Department of Mathematics, University of Delhi, Delhi - 110007 (INDIA).
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.
http://www.kjm-math.org/article_86133_d0ddc2ce6b15b61ebf8dd33d6d518696.pdf
Toeplitz operator
slant Toeplitz operator
bidisk
Torus
eng
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
2423-4788
2019-07-01
5
2
77
95
10.22034/kjm.2018.68796
88074
Conformal Semi-Invariant Submersions from Almost Contact Metric Manifolds onto Riemannian Manifolds
Rajendra Prasad
rp.manpur@rediffmail.com
1
Sushil Kumar
sushilmath20@gmail.com
2
Department of mathematics and Astronomy, University of Lucknow, Lucknow, India
Department of mathematics and Astronomy, University of Lucknow, Lucknow, India
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.
http://www.kjm-math.org/article_88074_f69b8a26e1688c8808176fbc7ab43cde.pdf
Riemannian submersion
anti-invariant submersion
conformal semi-invariant submersions
eng
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
2423-4788
2019-07-01
5
2
96
107
10.22034/kjm.2019.88082
88082
Local Convergence of a Novel Eighth Order Method under Hypotheses Only on the First Derivative
Ioannis Argyros
iargyros@cameron.edu
1
Santhosh George
sgeorge@nitk.edu.in
2
Shobha Erappa
shobha.me@gmail.com
3
Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
Department of Mathematical and Computational Sciences, NIT Karnataka, 575 025, India
Department of Mathematics, Manipal Institute of Technology, Manipal, Karnataka, 576104, India
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.
http://www.kjm-math.org/article_88082_705a0abeb572a4da9c9b55a24aaf5217.pdf
Eighth order of convergence
ball convergence
Banach space
Frechet-derivative
eng
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
2423-4788
2019-07-01
5
2
108
112
10.22034/kjm.2019.88084
88084
On Certain Conditions for Convex Optimization in Hilbert Spaces
Benard Okelo
bnyaare@yahoo.com
1
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.
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.
http://www.kjm-math.org/article_88084_b5eebff35178eb5f92b22a462b6c4f8b.pdf
Optimization problem
convex function
Hilbert space
eng
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
2423-4788
2019-07-01
5
2
113
123
10.22034/kjm.2019.88426
88426
Proximal Point Algorithms for Finding Common Fixed Points of a Finite Family of Nonexpansive Multivalued Mappings in Real Hilbert Spaces
Akindele Mebawondu
dele@aims.ac.za
1
School of Mathematics, Statistics and Computer Science, University of KwaZuluNatal, Durban, South Africa
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.
http://www.kjm-math.org/article_88426_f7ea9c7dc575d3815a88a6312c349e52.pdf
Proximal point algorithms
fixed point
multivalued nonexpansive mapping
Hilbert space
eng
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
2423-4788
2019-07-01
5
2
124
131
10.22034/kjm.2019.88427
88427
On Starlikeness, Convexity, and Close-to-Convexity of Hyper-Bessel Function
İbrahim Aktaş
aktasibrahim38@gmail.com
1
Department of Mathematics, Kamil Özdağ Science Faculty, Karamanoğlu Mehmetbey Uninersity, Karaman, Turkey.
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.
http://www.kjm-math.org/article_88427_8d40602648d983ede04029651f1117c4.pdf
Analytic function
hyper-Bessel function
Starlike
convex and close-to-convex functions
eng
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
2423-4788
2019-07-01
5
2
132
138
10.22034/kjm.2019.88428
88428
Convergence of Operators with Closed Range
P. Johnson
nitksam@gmail.com
1
S. Balaji
balajimath@gmail.com
2
Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Surathkal, Karnataka - 575 025, India.
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamilnadu - 632 014, India.
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.
http://www.kjm-math.org/article_88428_0bd9bda9f59db84efd3662be88f82bc7.pdf
Frechet spaces
closed range operators
Moore-Penrose inverses