Certain Results on Starlike and Close-to-Convex Functions
Pardeep
Kaur
Department of Applied Sciences, Baba Banda Singh Bahadur Engineering
College, Fatehgarh Sahib-140407, Punjab, India.
author
Sukhwinder
Billing
Department of Mathematics, Sri Guru Granth Shaib World University, Fatehgarh Sahib-140407, Punjab, India.
author
text
article
2019
eng
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.
Khayyam Journal of Mathematics
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)
2423-4788
5
v.
2
no.
2019
1
14
http://www.kjm-math.org/article_84141_ae4b8ee0e542e44c6a493733d70415a8.pdf
dx.doi.org/10.22034/kjm.2019.84141
Power Inequalities for the Numerical Radius of Operators in Hilbert Spaces
Mohammad
Rashid
Department of Mathematics and Statistics, Faculty of Science P.O.Box(7),
Mu’tah University, Alkarak-Jordan.
author
text
article
2019
eng
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 $\|x\|=1$.
Khayyam Journal of Mathematics
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)
2423-4788
5
v.
2
no.
2019
15
29
http://www.kjm-math.org/article_84204_a321253ff5f81d65f8472735f8eb5f80.pdf
dx.doi.org/10.22034/kjm.2019.84204
On General $( \alpha, \beta)$-Metrics with Some Curvature Properties
Bankteshwar
Tiwari
DST-CIMS, Institute of Science, Banaras Hindu University, Varanasi-221005,
India.
author
Ranadip
Gangopadhyay
DST-CIMS, Institute of Science, Banaras Hindu University, Varanasi-221005,
India.
author
Ghanashyam
Prajapati
Loknayak Jai Prakash Institute of Technology, Chhapra-841302, India.
author
text
article
2019
eng
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.
Khayyam Journal of Mathematics
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)
2423-4788
5
v.
2
no.
2019
30
39
http://www.kjm-math.org/article_84205_7a50131e4fbba322eb53ea4697d49b67.pdf
dx.doi.org/10.22034/kjm.2019.84205
Traces of Schur and Kronecker Products for Block Matrices
Ismael
García-Bayona
Departamento de Análisis Matemático, Universidad de Valencia, 46100 Burjassot, Valencia, Spain.
author
text
article
2019
eng
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.
Khayyam Journal of Mathematics
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)
2423-4788
5
v.
2
no.
2019
40
50
http://www.kjm-math.org/article_84207_18a097d3d32ba04b3cab1968f04ce4ff.pdf
dx.doi.org/10.22034/kjm.2019.84207
Direct Estimates for Stancu Variant of Lupaş-Durrmeyer Operators Based On Polya Distribution
Lakshmi
Mishra
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT) University, Vellore 632 014, Tamil Nadu, India.
author
Alok
Kumar
Department of Computer Science, Dev Sanskriti Vishwavidyalaya, Haridwar-
249411, Uttarakhand, India.
author
text
article
2019
eng
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.
Khayyam Journal of Mathematics
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)
2423-4788
5
v.
2
no.
2019
51
64
http://www.kjm-math.org/article_85886_29d744acfffe5c453538e24c39189d1b.pdf
dx.doi.org/10.22034/kjm.2019.85886
Slant Toeplitz Operators on the Lebesgue Space of the Torus
Gopal
Datt
Department of Mathematics, PGDAV College, University of Delhi, Delhi-110065 (INDIA).
author
Neelima
Ohri
Department of Mathematics, University of Delhi, Delhi - 110007 (INDIA).
author
text
article
2019
eng
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.
Khayyam Journal of Mathematics
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)
2423-4788
5
v.
2
no.
2019
65
76
http://www.kjm-math.org/article_86133_d0ddc2ce6b15b61ebf8dd33d6d518696.pdf
dx.doi.org/10.22034/kjm.2019.86133
Conformal Semi-Invariant Submersions from Almost Contact Metric Manifolds onto Riemannian Manifolds
Rajendra
Prasad
Department of mathematics and Astronomy, University of Lucknow, Lucknow, India
author
Sushil
Kumar
Department of mathematics and Astronomy, University of Lucknow, Lucknow, India
author
text
article
2019
eng
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.
Khayyam Journal of Mathematics
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)
2423-4788
5
v.
2
no.
2019
77
95
http://www.kjm-math.org/article_88074_f69b8a26e1688c8808176fbc7ab43cde.pdf
dx.doi.org/10.22034/kjm.2018.68796
Local Convergence of a Novel Eighth Order Method under Hypotheses Only on the First Derivative
Ioannis
Argyros
Department of Mathematical Sciences, Cameron University, Lawton, OK
73505, USA
author
Santhosh
George
Department of Mathematical and Computational Sciences, NIT Karnataka,
575 025, India
author
Shobha
Erappa
Department of Mathematics, Manipal Institute of Technology, Manipal,
Karnataka, 576104, India
author
text
article
2019
eng
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.
Khayyam Journal of Mathematics
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)
2423-4788
5
v.
2
no.
2019
96
107
http://www.kjm-math.org/article_88082_705a0abeb572a4da9c9b55a24aaf5217.pdf
dx.doi.org/10.22034/kjm.2019.88082
On Certain Conditions for Convex Optimization in Hilbert Spaces
Benard
Okelo
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.
author
text
article
2019
eng
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.
Khayyam Journal of Mathematics
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)
2423-4788
5
v.
2
no.
2019
108
112
http://www.kjm-math.org/article_88084_b5eebff35178eb5f92b22a462b6c4f8b.pdf
dx.doi.org/10.22034/kjm.2019.88084
Proximal Point Algorithms for Finding Common Fixed Points of a Finite Family of Nonexpansive Multivalued Mappings in Real Hilbert Spaces
Akindele
Mebawondu
School of Mathematics, Statistics and Computer Science, University of KwaZuluNatal, Durban, South Africa
author
text
article
2019
eng
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.
Khayyam Journal of Mathematics
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)
2423-4788
5
v.
2
no.
2019
113
123
http://www.kjm-math.org/article_88426_f7ea9c7dc575d3815a88a6312c349e52.pdf
dx.doi.org/10.22034/kjm.2019.88426
On Starlikeness, Convexity, and Close-to-Convexity of Hyper-Bessel Function
İbrahim
Aktaş
Department of Mathematics, Kamil Özdağ Science Faculty, Karamanoğlu Mehmetbey Uninersity, Karaman, Turkey.
author
text
article
2019
eng
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.
Khayyam Journal of Mathematics
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)
2423-4788
5
v.
2
no.
2019
124
131
http://www.kjm-math.org/article_88427_8d40602648d983ede04029651f1117c4.pdf
dx.doi.org/10.22034/kjm.2019.88427
Convergence of Operators with Closed Range
P.
Johnson
Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Surathkal, Karnataka - 575 025, India.
author
S.
Balaji
Department of Mathematics, School of Advanced Sciences, Vellore Institute
of Technology, Vellore, Tamilnadu - 632 014, India.
author
text
article
2019
eng
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.
Khayyam Journal of Mathematics
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)
2423-4788
5
v.
2
no.
2019
132
138
http://www.kjm-math.org/article_88428_0bd9bda9f59db84efd3662be88f82bc7.pdf
dx.doi.org/10.22034/kjm.2019.88428