ORIGINAL_ARTICLE
Certain Results on Starlike and Close-to-Convex Functions
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
2019-07-01T11:23:20
2019-07-16T11:23:20
1
14
10.22034/kjm.2019.84141
starlike function
close-to-convex function
Bazilevič function
differential subordination
Pardeep
Kaur
aradhitadhiman@gmail.com
true
1
Department of Applied Sciences, Baba Banda Singh Bahadur Engineering
College, Fatehgarh Sahib-140407, Punjab, India.
Department of Applied Sciences, Baba Banda Singh Bahadur Engineering
College, Fatehgarh Sahib-140407, Punjab, India.
Department of Applied Sciences, Baba Banda Singh Bahadur Engineering
College, Fatehgarh Sahib-140407, Punjab, India.
LEAD_AUTHOR
Sukhwinder
Billing
ssbilling@gmail.com
true
2
Department of Mathematics, Sri Guru Granth Shaib World University, Fatehgarh Sahib-140407, Punjab, India.
Department of Mathematics, Sri Guru Granth Shaib World University, Fatehgarh Sahib-140407, Punjab, India.
Department of Mathematics, Sri Guru Granth Shaib World University, Fatehgarh Sahib-140407, Punjab, India.
AUTHOR
ORIGINAL_ARTICLE
Power Inequalities for the Numerical Radius of Operators in Hilbert Spaces
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 $\|x\|=1$.
http://www.kjm-math.org/article_84204_a321253ff5f81d65f8472735f8eb5f80.pdf
2019-07-01T11:23:20
2019-07-16T11:23:20
15
29
10.22034/kjm.2019.84204
Numerical Range
Numerical radius
Aluthge transformation
strongly convex
Mohammad
Rashid
malik_okasha@yahoo.com
true
1
Department of Mathematics and Statistics, Faculty of Science P.O.Box(7),
Mu’tah University, Alkarak-Jordan.
Department of Mathematics and Statistics, Faculty of Science P.O.Box(7),
Mu’tah University, Alkarak-Jordan.
Department of Mathematics and Statistics, Faculty of Science P.O.Box(7),
Mu’tah University, Alkarak-Jordan.
AUTHOR
ORIGINAL_ARTICLE
On General $( \alpha, \beta)$-Metrics with Some Curvature Properties
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
2019-07-01T11:23:20
2019-07-16T11:23:20
30
39
10.22034/kjm.2019.84205
Finsler space
General (α, β)-metric
Ξ-curvature
$H$-curvature
Bankteshwar
Tiwari
banktesht@gmail.com
true
1
DST-CIMS, Institute of Science, Banaras Hindu University, Varanasi-221005,
India.
DST-CIMS, Institute of Science, Banaras Hindu University, Varanasi-221005,
India.
DST-CIMS, Institute of Science, Banaras Hindu University, Varanasi-221005,
India.
AUTHOR
Ranadip
Gangopadhyay
gangulyranadip@gmail.com
true
2
DST-CIMS, Institute of Science, Banaras Hindu University, Varanasi-221005,
India.
DST-CIMS, Institute of Science, Banaras Hindu University, Varanasi-221005,
India.
DST-CIMS, Institute of Science, Banaras Hindu University, Varanasi-221005,
India.
LEAD_AUTHOR
Ghanashyam
Prajapati
gspbhu@gmail.com
true
3
Loknayak Jai Prakash Institute of Technology, Chhapra-841302, India.
Loknayak Jai Prakash Institute of Technology, Chhapra-841302, India.
Loknayak Jai Prakash Institute of Technology, Chhapra-841302, India.
AUTHOR
ORIGINAL_ARTICLE
Traces of Schur and Kronecker Products for Block Matrices
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
2019-07-01T11:23:20
2019-07-16T11:23:20
40
50
10.22034/kjm.2019.84207
Schur product
Kronecker product
Trace
matrix multiplication
inequalities
Ismael
García-Bayona
garbais@uv.es
true
1
Departamento de Análisis Matemático, Universidad de Valencia, 46100 Burjassot, Valencia, Spain.
Departamento de Análisis Matemático, Universidad de Valencia, 46100 Burjassot, Valencia, Spain.
Departamento de Análisis Matemático, Universidad de Valencia, 46100 Burjassot, Valencia, Spain.
AUTHOR
ORIGINAL_ARTICLE
Direct Estimates for Stancu Variant of Lupaş-Durrmeyer Operators Based On Polya Distribution
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
2019-07-01T11:23:20
2019-07-16T11:23:20
51
64
10.22034/kjm.2019.85886
Asymptotic formula
Modulus of continuity
$K$-functional
Polya distribution
local approximation
Lakshmi
Mishra
lakshminarayanmishra04@gmail.com
true
1
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT) University, Vellore 632 014, Tamil Nadu, India.
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT) University, Vellore 632 014, Tamil Nadu, India.
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT) University, Vellore 632 014, Tamil Nadu, India.
LEAD_AUTHOR
Alok
Kumar
alokkpma@gmail.com
true
2
Department of Computer Science, Dev Sanskriti Vishwavidyalaya, Haridwar-
249411, Uttarakhand, India.
Department of Computer Science, Dev Sanskriti Vishwavidyalaya, Haridwar-
249411, Uttarakhand, India.
Department of Computer Science, Dev Sanskriti Vishwavidyalaya, Haridwar-
249411, Uttarakhand, India.
AUTHOR
ORIGINAL_ARTICLE
Slant Toeplitz Operators on the Lebesgue Space of the Torus
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
2019-07-01T11:23:20
2019-07-16T11:23:20
65
76
10.22034/kjm.2019.86133
Toeplitz operator
slant Toeplitz operator
bidisk
Torus
Gopal
Datt
gopal.d.sati@gmail.com
true
1
Department of Mathematics, PGDAV College, University of Delhi, Delhi-110065 (INDIA).
Department of Mathematics, PGDAV College, University of Delhi, Delhi-110065 (INDIA).
Department of Mathematics, PGDAV College, University of Delhi, Delhi-110065 (INDIA).
AUTHOR
Neelima
Ohri
neelimaohri1990@gmail.com
true
2
Department of Mathematics, University of Delhi, Delhi - 110007 (INDIA).
Department of Mathematics, University of Delhi, Delhi - 110007 (INDIA).
Department of Mathematics, University of Delhi, Delhi - 110007 (INDIA).
LEAD_AUTHOR
ORIGINAL_ARTICLE
Conformal Semi-Invariant Submersions from Almost Contact Metric Manifolds onto Riemannian Manifolds
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
2019-07-01T11:23:20
2019-07-16T11:23:20
77
95
10.22034/kjm.2018.68796
Riemannian submersion
anti-invariant submersion
conformal semi-invariant submersions
Rajendra
Prasad
rp.manpur@rediffmail.com
true
1
Department of mathematics and Astronomy, University of Lucknow, Lucknow, India
Department of mathematics and Astronomy, University of Lucknow, Lucknow, India
Department of mathematics and Astronomy, University of Lucknow, Lucknow, India
AUTHOR
Sushil
Kumar
sushilmath20@gmail.com
true
2
Department of mathematics and Astronomy, University of Lucknow, Lucknow, India
Department of mathematics and Astronomy, University of Lucknow, Lucknow, India
Department of mathematics and Astronomy, University of Lucknow, Lucknow, India
LEAD_AUTHOR
ORIGINAL_ARTICLE
Local Convergence of a Novel Eighth Order Method under Hypotheses Only on the First Derivative
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
2019-07-01T11:23:20
2019-07-16T11:23:20
96
107
10.22034/kjm.2019.88082
Eighth order of convergence
ball convergence
Banach space
Frechet-derivative
Ioannis
Argyros
iargyros@cameron.edu
true
1
Department of Mathematical Sciences, Cameron University, Lawton, OK
73505, USA
Department of Mathematical Sciences, Cameron University, Lawton, OK
73505, USA
Department of Mathematical Sciences, Cameron University, Lawton, OK
73505, USA
AUTHOR
Santhosh
George
sgeorge@nitk.ac.in
true
2
Department of Mathematical and Computational Sciences, NIT Karnataka,
575 025, India
Department of Mathematical and Computational Sciences, NIT Karnataka,
575 025, India
Department of Mathematical and Computational Sciences, NIT Karnataka,
575 025, India
AUTHOR
Shobha
Erappa
shobha.me@gmail.com
true
3
Department of Mathematics, Manipal Institute of Technology, Manipal,
Karnataka, 576104, India
Department of Mathematics, Manipal Institute of Technology, Manipal,
Karnataka, 576104, India
Department of Mathematics, Manipal Institute of Technology, Manipal,
Karnataka, 576104, India
LEAD_AUTHOR
ORIGINAL_ARTICLE
On Certain Conditions for Convex Optimization in Hilbert Spaces
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.
http://www.kjm-math.org/article_88084_b5eebff35178eb5f92b22a462b6c4f8b.pdf
2019-07-01T11:23:20
2019-07-16T11:23:20
108
112
10.22034/kjm.2019.88084
Optimization problem
convex function
Hilbert space
Benard
Okelo
bnyaare@yahoo.com
true
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.
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.
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.
LEAD_AUTHOR
ORIGINAL_ARTICLE
Proximal Point Algorithms for Finding Common Fixed Points of a Finite Family of Nonexpansive Multivalued Mappings in Real Hilbert Spaces
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.
http://www.kjm-math.org/article_88426_f7ea9c7dc575d3815a88a6312c349e52.pdf
2019-07-01T11:23:20
2019-07-16T11:23:20
113
123
10.22034/kjm.2019.88426
Proximal point algorithms
fixed point
multivalued nonexpansive mapping
Hilbert space
Akindele
Mebawondu
dele@aims.ac.za
true
1
School of Mathematics, Statistics and Computer Science, University of KwaZuluNatal, Durban, South Africa
School of Mathematics, Statistics and Computer Science, University of KwaZuluNatal, Durban, South Africa
School of Mathematics, Statistics and Computer Science, University of KwaZuluNatal, Durban, South Africa
LEAD_AUTHOR
ORIGINAL_ARTICLE
On Starlikeness, Convexity, and Close-to-Convexity of Hyper-Bessel Function
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
2019-07-01T11:23:20
2019-07-16T11:23:20
124
131
10.22034/kjm.2019.88427
Analytic function
hyper-Bessel function
Starlike
convex and close-to-convex functions
İbrahim
Aktaş
aktasibrahim38@gmail.com
true
1
Department of Mathematics, Kamil Özdağ Science Faculty, Karamanoğlu Mehmetbey Uninersity, Karaman, Turkey.
Department of Mathematics, Kamil Özdağ Science Faculty, Karamanoğlu Mehmetbey Uninersity, Karaman, Turkey.
Department of Mathematics, Kamil Özdağ Science Faculty, Karamanoğlu Mehmetbey Uninersity, Karaman, Turkey.
LEAD_AUTHOR
ORIGINAL_ARTICLE
Convergence of Operators with Closed Range
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
2019-07-01T11:23:20
2019-07-16T11:23:20
132
138
10.22034/kjm.2019.88428
Frechet spaces
closed range operators
Moore-Penrose inverses
P.
Johnson
nitksam@gmail.com
true
1
Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Surathkal, Karnataka - 575 025, India.
Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Surathkal, Karnataka - 575 025, India.
Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Surathkal, Karnataka - 575 025, India.
LEAD_AUTHOR
S.
Balaji
balajimath@gmail.com
true
2
Department of Mathematics, School of Advanced Sciences, Vellore Institute
of Technology, Vellore, Tamilnadu - 632 014, India.
Department of Mathematics, School of Advanced Sciences, Vellore Institute
of Technology, Vellore, Tamilnadu - 632 014, India.
Department of Mathematics, School of Advanced Sciences, Vellore Institute
of Technology, Vellore, Tamilnadu - 632 014, India.
AUTHOR