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 Mathematics2423-47885220190701Certain Results on Starlike and Close-to-Convex Functions1148414110.22034/kjm.2019.84141ENPardeepKaurDepartment of Applied Sciences, Baba Banda Singh Bahadur Engineering
College, Fatehgarh Sahib-140407, Punjab, India.Sukhwinder SinghBillingDepartment of Mathematics, Sri Guru Granth Shaib World University, Fatehgarh Sahib-140407, Punjab, India.Journal Article20180305Using 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.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 Mathematics2423-47885220190701Power Inequalities for the Numerical Radius of Operators in Hilbert Spaces15298420410.22034/kjm.2019.84204ENMohammad H.M.RashidDepartment of Mathematics and Statistics, Faculty of Science P.O.Box(7),
Mu’tah University, Alkarak-Jordan.Journal Article20180802We 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 $|x|=1$.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 Mathematics2423-47885220190701On General $( alpha, beta)$-Metrics with Some Curvature Properties30398420510.22034/kjm.2019.84205ENBankteshwarTiwariDST-CIMS, Institute of Science, Banaras Hindu University, Varanasi-221005,
India.RanadipGangopadhyayDST-CIMS, Institute of Science, Banaras Hindu University, Varanasi-221005,
India.0000-0003-0989-3143Ghanashyam Kr.PrajapatiLoknayak Jai Prakash Institute of Technology, Chhapra-841302, India.Journal Article20180924In 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.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 Mathematics2423-47885220190701Traces of Schur and Kronecker Products for Block Matrices40508420710.22034/kjm.2019.84207ENIsmaelGarcía-BayonaDepartamento de Análisis Matemático, Universidad de Valencia, 46100 Burjassot, Valencia, Spain.0000-0003-1027-5086Journal Article20181008In 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.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 Mathematics2423-47885220190701Direct Estimates for Stancu Variant of Lupaş-Durrmeyer Operators Based On Polya Distribution51648588610.22034/kjm.2019.85886ENLakshmi NarayanMishraDepartment of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT) University, Vellore 632 014, Tamil Nadu, India.0000-0001-7774-7290AlokKumarDepartment of Computer Science, Dev Sanskriti Vishwavidyalaya, Haridwar-
249411, Uttarakhand, India.0000-0002-5171-1393Journal Article20180913In 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.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 Mathematics2423-47885220190701Slant Toeplitz Operators on the Lebesgue Space of the Torus65768613310.22034/kjm.2019.86133ENGopalDattDepartment of Mathematics, PGDAV College, University of Delhi, Delhi-110065 (INDIA).NeelimaOhriDepartment of Mathematics, University of Delhi, Delhi - 110007 (INDIA).Journal Article20180812This 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.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 Mathematics2423-47885220190701Conformal Semi-Invariant Submersions from Almost Contact Metric Manifolds onto Riemannian Manifolds77958807410.22034/kjm.2018.68796ENRajendraPrasadDepartment of mathematics and Astronomy, University of Lucknow, Lucknow, IndiaSushilKumarDepartment of mathematics and Astronomy, University of Lucknow, Lucknow, IndiaJournal Article20180612As 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.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 Mathematics2423-47885220190701Local Convergence of a Novel Eighth Order Method under Hypotheses Only on the First Derivative961078808210.22034/kjm.2019.88082ENIoannis K.ArgyrosDepartment of Mathematical Sciences, Cameron University, Lawton, OK
73505, USA0000-0002-9189-9298SanthoshGeorgeDepartment of Mathematical and Computational Sciences, NIT Karnataka,
575 025, India0000-0002-3530-5539Shobha M.ErappaDepartment of Mathematics, Manipal Institute of Technology, Manipal,
Karnataka, 576104, IndiaJournal Article20180618We 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.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 Mathematics2423-47885220190701On Certain Conditions for Convex Optimization in Hilbert Spaces1081128808410.22034/kjm.2019.88084ENBenardOkeloDepartment of Pure and Applied Mathematics, School of Mathematics and
Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology, Box 210-40601, Bondo-Kenya.0000 0001 2345 6789Journal Article20180713In 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.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 Mathematics2423-47885220190701Proximal Point Algorithms for Finding Common Fixed Points of a Finite Family of Nonexpansive Multivalued Mappings in Real Hilbert Spaces1131238842610.22034/kjm.2019.88426ENAkindele AdebayoMebawonduSchool of Mathematics, Statistics and Computer Science, University of KwaZuluNatal, Durban, South AfricaJournal Article20180712We 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.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 Mathematics2423-47885220190701On Starlikeness, Convexity, and Close-to-Convexity of Hyper-Bessel Function1241318842710.22034/kjm.2019.88427ENİbrahimAktaşDepartment of Mathematics, Kamil Özdağ Science Faculty, Karamanoğlu Mehmetbey Uninersity, Karaman, Turkey.0000-0003-4570-4485Journal Article20181221In 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.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 Mathematics2423-47885220190701Convergence of Operators with Closed Range1321388842810.22034/kjm.2019.88428ENP. SamJohnsonDepartment of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Surathkal, Karnataka - 575 025, India.0000-0003-3461-5380S.BalajiDepartment of Mathematics, School of Advanced Sciences, Vellore Institute
of Technology, Vellore, Tamilnadu - 632 014, India.Journal Article20190720Izumino 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.