Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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  • 2023-04-30

    On sharp general coefficient estimates for $\vartheta$-spirallike functions

    \c{S}ahsene Altinkaya, Tu\u{g}ba Yavuz

    Abstract : This paper attempts to investigate a new subfamily \linebreak $\mathcal{ST}_{\vartheta ,\sigma}\left( \alpha ,\beta ,\gamma ,\mu \right) $ of spirallike functions endowed with Mittag-Leffler and Wright functions. The paper further investigates sharp coefficient bounds for functions that belong to this class.

  • 2023-10-31

    Joint essential numerical spectrum and Jeribi essential numerical spectrum of linear operators in Banach spaces

    Bouthaina Abdelhedi, Wissal Boubaker, Nedra Moalla

    Abstract : The purpose of this paper is to introduce the concept of joint essential numerical spectrum $\sigma_{en}(\cdot)$ of $q$-tuple of operators on a Banach space and to study its properties. This notion generalize the notion of the joint essential numerical range.

  • 2023-07-31

    $\star$-conformal Ricci solitons on almost coK\"{a}hler manifolds

    Tarak Mandal, Avijit Sarkar

    Abstract : The main intention of the current paper is to characterize certain properties of $\star$-conformal Ricci solitons on non-coK\"ahler $(\kappa,\mu)$-almost coK\"{a}hler manifolds. At first, we find that there does not exist $\star$-conformal Ricci soliton if the potential vector field is the Reeb vector field $\theta$. We also prove that the non-coK\"ahler $(\kappa,\mu)$-almost coK\"ahler manifolds admit $\star$-conformal Ricci solitons if the potential vector field is the infinitesimal contact transformation. It is also studied that there does not exist $\star$-conformal gradient Ricci solitons on the said manifolds. An example has been constructed to verify the obtained results.

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  • 2022-07-31

    Geometric distance fitting of parabolas in $mathbb{R}^3$

    Ik Sung Kim

    Abstract : We are interested in the problem of fitting a parabola to a set of data points in $mathbb{ R}^3 $. It can be usually solved by minimizing the geometric distances from the fitted parabola to the given data points. In this paper, a parabola fitting algorithm will be proposed in such a way that the sum of the squares of the geometric distances is minimized in~$mathbb{R}^3$. Our algorithm is mainly based on the steepest descent technique which determines an adequate number $ lambda $ such that $h ( lambda ) = Q ( u - lambda abla Qigl( u igr) ) < Q ( u)$. Some numerical examples are given to test our algorithm.

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  • 2022-07-31

    Estimates for the norm of a multilinear form on $mathbb{R}^n$ with the $l_p$-norm

    Sung Guen Kim

    Abstract : In this paper, we present some estimates for the norm of a multilinear form $Tin {mathcal L}(^ml_{p}^n)$ for $1leq pleqinfty$ and $n, mgeq 2.$

  • 2023-07-31

    Areas of polygons with vertices from Lucas sequences on a plane

    SeokJun Hong, SiHyun Moon, Ho Park, SeoYeon Park, SoYoung Seo

    Abstract : Area problems for triangles and polygons whose vertices have Fibonacci numbers on a plane were presented by A. Shriki, O. Liba, and S. Edwards et al. In 2017, V. P. Johnson and C. K. Cook addressed problems of the areas of triangles and polygons whose vertices have various sequences. This paper examines the conditions of triangles and polygons whose vertices have Lucas sequences and presents a formula for their areas.

  • 2024-04-30

    Horadam polynomials for a new subclass of Sakaguchi-type bi-univalent functions defined by $({p},{q})$-derivative operator

    Vanithakumari B , SARAVANAN G , Baskaran S , Sibel Yalcin

    Abstract : In this paper, a new subclass, $\mathcal{SC}_{\sigma}^{\mu,{p},{q}}({r},{s};x)$, of Sakaguchi-type analytic bi-univalent functions defined by $({p},{q})$-derivative operator using Horadam polynomials is constructed and investigated. The initial coefficient bounds for $|a_{2}|$ and $|a_{3}|$ are obtained. Fekete-Szeg\"{o} inequalities for the class are found. Finally, we give some corollaries.

  • 2023-01-31

    Hyperbolic structure of pointwise inverse pseudo-orbit tracing property for $C^1$ diffeomorphisms

    Manseob Lee

    Abstract : We deal with a type of inverse pseudo-orbit tracing property with respect to the class of continuous methods, as suggested and studied by Pilyugin \cite{P1}. In this paper, we consider a continuous method induced through the diffeomorphism of a compact smooth manifold, and using the concept, we proved the following: (i) If a diffeomorphism $f$ of a compact smooth manifold $M$ has the robustly pointwise inverse pseudo-orbit tracing property, $f$ is structurally stable. (ii) For a $C^1$ generic diffeomorphism $f$ of a compact smooth manifold $M$, if $f$ has the pointwise inverse pseudo-orbit tracing property, $f$ is structurally stable. (iii) If a diffeomorphism $f$ has the robustly pointwise inverse pseudo-orbit tracing property around a transitive set $\Lambda$, then $\Lambda$ is hyperbolic for $f$. Finally, (iv) for $C^1$ generically, if a diffeomorphism $f$ has the pointwise inverse pseudo-orbit tracing property around a locally maximal transitive set $\Lambda$, then $\Lambda$ is hyperbolic for $f$. In addition, we investigate cases of volume preserving diffeomorphisms.

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  • 2022-10-31

    Ground state sign-changing solutions for nonlinear Schr\"{o}dinger-Poisson system with indefinite potentials

    Shubin Yu, Ziheng Zhang

    Abstract : This paper is concerned with the following Schr\"{o}dinger-\linebreak Poisson system$$\left\{\begin{array}{ll} -{\Delta}u+V(x)u+K(x){\phi}u=a(x)|u|^{p-2}u  &\mbox{in}\ \mathbb{R}^3, \\[0.1cm] -{\Delta}{\phi}=K(x)u^{2}&\mbox{in}\ \mathbb{R}^3, \\[0.1cm]\end{array}\right.$$where $4<p<6$. For the case that $K$ is nonnegative, $V$ and $a$ are indefinite, we prove the above problem possesses one ground state sign-changing solutionwith exactly two nodal domains by constraint variational method and quantitative deformation lemma. Moreover, we show that the energy of sign-changing solutions islarger than that of the ground state solutions. The novelty of this paper is that the potential $a$ is indefinite and allowed to vanish at infinity. In this sense, we complementthe existing results obtained by Batista and Furtado \cite{BF18}.

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  • 2024-01-31

    Conformal Ricci soliton on paracontact metric $(k,\mu)$-manifolds with Schouten-van Kampen connection

    PARDIP MANDAL, MOHAMMAD HASAN SHAHID, SARVESH KUMAR YADAV

    Abstract : The main object of the present paper is to study conformal Ricci soliton on paracontact metric $(k,\mu)$-manifolds with respect to Schouten-van Kampen connection. Further, we obtain the result when paracontact metric $(k,\mu)$-manifolds with respect to Schouten-van Kampen connection satisfying the condition $\overset{\star}{C}(\xi,U)\cdot\overset{\star}{S}=0$. Finally we characterized concircular curvature tensor on paracontact metric $(k,\mu)$-manifolds with respect to Schouten-van Kampen connection.

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April, 2024
Vol.39 No.2

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