2019
5
2
2
0
Certain Results on Starlike and ClosetoConvex Functions
2
2
Using the technique of differential subordination, we here, obtain certain sufficient conditions for starlike and closetoconvex functions. In most of the results obtained here, the region of variability of the differential operators implying starlikeness and closetoconvexity of analytic functions has been extended. The extended regions of the operators have been shown pictorially.
1

1
14


Pardeep
Kaur
Department of Applied Sciences, Baba Banda Singh Bahadur Engineering
College, Fatehgarh Sahib140407, Punjab, India.
Department of Applied Sciences, Baba Banda
India
aradhitadhiman@gmail.com


Sukhwinder
Billing
Department of Mathematics, Sri Guru Granth Shaib World University, Fatehgarh Sahib140407, Punjab, India.
Department of Mathematics, Sri Guru Granth
India
ssbilling@gmail.com
starlike function
closetoconvex function
Bazilevič function
differential subordination
Power Inequalities for the Numerical Radius of Operators in Hilbert Spaces
2
2
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 HölderMcCarthy 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 selfadjoint operator on the Hilbert space $cal{H}$ with $sigma(T)subset {rm int}(J)$, then $$langle T^2x,xranglelangle Tx,xrangle^2leq dfrac{1}{2c}(langle f'(T)Tx,xrangle langle Tx,xrangle langle f'(T)x,xrangle)$$ for each $xincal{H}$, with $x=1$.
1

15
29


Mohammad
Rashid
Department of Mathematics and Statistics, Faculty of Science P.O.Box(7),
Mu’tah University, AlkarakJordan.
Department of Mathematics and Statistics,
Jordan
malik_okasha@yahoo.com
Numerical Range
Numerical radius
Aluthge transformation
strongly convex
On General $( alpha, beta)$Metrics with Some Curvature Properties
2
2
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 Hcurvature. 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.
1

30
39


Bankteshwar
Tiwari
DSTCIMS, Institute of Science, Banaras Hindu University, Varanasi221005,
India.
DSTCIMS, Institute of Science, Banaras Hindu
India
banktesht@gmail.com


Ranadip
Gangopadhyay
DSTCIMS, Institute of Science, Banaras Hindu University, Varanasi221005,
India.
DSTCIMS, Institute of Science, Banaras Hindu
India
gangulyranadip@gmail.com


Ghanashyam
Prajapati
Loknayak Jai Prakash Institute of Technology, Chhapra841302, India.
Loknayak Jai Prakash Institute of Technology,
India
gspbhu@gmail.com
Finsler space
General (α, β)metric
Ξcurvature
$H$curvature
Traces of Schur and Kronecker Products for Block Matrices
2
2
In this paper, we define two new Schur and Kroneckertype 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 submultiplicative for them. Also, versions in the block matrix framework of results of Das, Vashisht, Taskara and Gumus will be obtained.
1

40
50


Ismael
GarcíaBayona
Departamento de Análisis Matemático, Universidad de Valencia, 46100 Burjassot, Valencia, Spain.
Departamento de Análisis Matemático,
Spain
garbais@uv.es
Schur product
Kronecker product
Trace
matrix multiplication
inequalities
Direct Estimates for Stancu Variant of LupaşDurrmeyer Operators Based On Polya Distribution
2
2
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.
1

51
64


Lakshmi
Mishra
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
India
lakshminarayanmishra04@gmail.com


Alok
Kumar
Department of Computer Science, Dev Sanskriti Vishwavidyalaya, Haridwar
249411, Uttarakhand, India.
Department of Computer Science, Dev Sanskriti
India
alokkpma@gmail.com
Asymptotic formula
Modulus of continuity
$K$functional
Polya distribution
local approximation
Slant Toeplitz Operators on the Lebesgue Space of the Torus
2
2
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.
1

65
76


Gopal
Datt
Department of Mathematics, PGDAV College, University of Delhi, Delhi110065 (INDIA).
Department of Mathematics, PGDAV College,
India
gopal.d.sati@gmail.com


Neelima
Ohri
Department of Mathematics, University of Delhi, Delhi  110007 (INDIA).
Department of Mathematics, University of
India
neelimaohri1990@gmail.com
Toeplitz operator
slant Toeplitz operator
bidisk
Torus
Conformal SemiInvariant Submersions from Almost Contact Metric Manifolds onto Riemannian Manifolds
2
2
As a generalization of semiinvariant Riemannian submersions, we introduce conformal semiinvariant submersions from almost contact metric manifolds onto Riemannian manifolds and study such submersions from Cosymplectic manifolds onto Riemannian manifolds. Examples of conformal semiinvariant submersions in which structure vector field is vertical are given. We study geometry of foliations determined by distributions involved in definition of conformal antiinvariant submersions. We also study the harmonicity of such submersions and find necessary and sufficient conditions for the distributions to be totally geodesic.
1

77
95


Rajendra
Prasad
Department of mathematics and Astronomy, University of Lucknow, Lucknow, India
Department of mathematics and Astronomy,
India
rp.manpur@rediffmail.com


Sushil
Kumar
Department of mathematics and Astronomy, University of Lucknow, Lucknow, India
Department of mathematics and Astronomy,
India
sushilmath20@gmail.com
Riemannian submersion
antiinvariant submersion
conformal semiinvariant submersions
Local Convergence of a Novel Eighth Order Method under Hypotheses Only on the First Derivative
2
2
We expand the applicability of eighth orderiterative 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 Frechetderivative. 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.
1

96
107


Ioannis
Argyros
Department of Mathematical Sciences, Cameron University, Lawton, OK
73505, USA
Department of Mathematical Sciences, Cameron
United States
iargyros@cameron.edu


Santhosh
George
Department of Mathematical and Computational Sciences, NIT Karnataka,
575 025, India
Department of Mathematical and Computational
India
sgeorge@nitk.edu.in


Shobha
Erappa
Department of Mathematics, Manipal Institute of Technology, Manipal,
Karnataka, 576104, India
Department of Mathematics, Manipal Institute
India
shobha.me@gmail.com
Eighth order of convergence
ball convergence
Banach space
Frechetderivative
On Certain Conditions for Convex Optimization in Hilbert Spaces
2
2
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.
1

108
112


Benard
Okelo
Department of Pure and Applied Mathematics, School of Mathematics and
Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology, Box 21040601, BondoKenya.
Department of Pure and Applied Mathematics,
Kenya
bnyaare@yahoo.com
Optimization problem
convex function
Hilbert space
Proximal Point Algorithms for Finding Common Fixed Points of a Finite Family of Nonexpansive Multivalued Mappings in Real Hilbert Spaces
2
2
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.
1

113
123


Akindele
Mebawondu
School of Mathematics, Statistics and Computer Science, University of KwaZuluNatal, Durban, South Africa
School of Mathematics, Statistics and Computer
South Africa
dele@aims.ac.za
Proximal point algorithms
fixed point
multivalued nonexpansive mapping
Hilbert space
On Starlikeness, Convexity, and ClosetoConvexity of HyperBessel Function
2
2
In the present investigation, our main aim is to derive some conditions on starlikeness, convexity, and closetoconvexity of normalized hyperBessel functions. Also we give some similar results for classical Bessel functions by using the relationships between hyperBessel and Bessel functions. As a result of the obtained conditions, some examples are also given.
1

124
131


İbrahim
Aktaş
Department of Mathematics, Kamil Özdağ Science Faculty, Karamanoğlu Mehmetbey Uninersity, Karaman, Turkey.
Department of Mathematics, Kamil Özdağ
Turkey
aktasibrahim38@gmail.com
Analytic function
hyperBessel function
Starlike
convex and closetoconvex functions
Convergence of Operators with Closed Range
2
2
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 MoorePenrose 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.
1

132
138


P.
Johnson
Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Surathkal, Karnataka  575 025, India.
Department of Mathematical and Computational
India
nitksam@gmail.com


S.
Balaji
Department of Mathematics, School of Advanced Sciences, Vellore Institute
of Technology, Vellore, Tamilnadu  632 014, India.
Department of Mathematics, School of Advanced
India
balajimath@gmail.com
Frechet spaces
closed range operators
MoorePenrose inverses