Communications of the
Korean Mathematical Society

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

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  • 2022-10-31

    Sharp estimates on the third order Hermitian-Toeplitz determinant for Sakaguchi classes

    Sushil Kumar, Virendra Kumar

    Abstract : In this paper, sharp lower and upper bounds on the third order Hermitian-Toeplitz determinant for the classes of Sakaguchi functions and some of its subclasses related to right-half of lemniscate of Bernoulli, reverse lemniscate of Bernoulli and exponential functions are investigated.

  • 2023-04-30

    Maximal chain of ideals and $n$-maximal ideal

    Hemin A. Ahmad, Parween A. Hummadi

    Abstract : In this paper, the concept of a maximal chain of ideals is introduced. Some properties of such chains are studied. We introduce some other concepts related to a maximal chain of ideals such as the $n$-maximal ideal, the maximal dimension of a ring $S$ $(M.\dim(S))$, the maximal depth of an ideal $K$ of $S$ $(M.d(K))$ and maximal height of an ideal $K(M.d(K))$.

  • 2022-10-31

    On strong exponential limit shadowing property

    Ali Darabi

    Abstract : In this study, we show that the strong exponential limit shadowing property (SELmSP, for short), which has been recently introduced, exists on a neighborhood of a hyperbolic set of a diffeomorphism. We also prove that $\Omega$-stable diffeomorphisms and $\mathcal{\mathcal{L}}$-hyperbolic homeomorphisms have this type of shadowing property. By giving examples, it is shown that this type of shadowing is different from the other shadowings, and the chain transitivity and chain mixing are not necessary for it. Furthermore, we extend this type of shadowing property to positively expansive maps with the shadowing property.

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  • 2022-10-31

    Classification of Solvable Lie groups whose non-trivial coadjoint orbits are of Codimension $1$

    Hieu Van Ha, Duong Quang Hoa, Vu Anh Le

    Abstract : We give a complete classification of simply connected and solvable real Lie groups whose nontrivial coadjoint orbits are of codimension 1. This classification of the Lie groups is one to one corresponding to the classification of their Lie algebras. Such a Lie group belongs to a class, called the class of MD-groups. The Lie algebra of an MD-group is called an MD-algebra. Some interest properties of MD-algebras will be investigated as well.

  • 2022-07-31

    Study of gradient solitons in three dimensional Riemannian manifolds

    Gour Gopal Biswas, Uday Chand De

    Abstract : We characterize a three-dimensional Riemannian manifold endowed with a type of semi-symmetric metric $P$-connection. At first, it is proven that if the metric of such a manifold is a gradient $m$-quasi-Einstein metric, then either the gradient of the potential function $psi$ is collinear with the vector field $P$ or, $lambda=-(m+2)$ and the manifold is of constant sectional curvature $-1$, provided $Ppsi eq m$. Next, it is shown that if the metric of the manifold under consideration is a gradient $ho$-Einstein soliton, then the gradient of the potential function is collinear with the vector field $P$. Also, we prove that if the metric of a 3-dimensional manifold with semi-symmetric metric $P$-connection is a gradient $omega$-Ricci soliton, then the manifold is of constant sectional curvature $-1$ and $lambda+mu=-2$. Finally, we consider an example to verify our results.

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  • 2022-04-30

    Fractional differential equations with nonlocal boundary conditions

    Agus L. Soenjaya

    Abstract : Existence and uniqueness for fractional differential equations satisfying a general nonlocal initial or boundary condition are proven by means of Schauder's fixed point theorem. The nonlocal condition is given as an integral with respect to a signed measure, and includes the standard initial value condition and multi-point boundary value condition.

  • 2022-01-31

    Toeplitz and Hankel operators with Carleson measure symbols

    Jaehui Park

    Abstract : In this paper, we introduce Toeplitz operators and Hankel operators with complex Borel measures on the closed unit disk. When a positive measure $mu$ on $(-1,1)$ is a Carleson measure, it is known that the corresponding Hankel matrix is bounded and vice versa. We show that for a positive measure $mu$ on $mathbb{D}$, $mu$ is a Carleson measure if and only if the Toeplitz operator with symbol $mu$ is a densely defined bounded linear operator. We also study Hankel operators of Hilbert--Schmidt class.

  • 2023-04-30

    Two linear polynomials shared by an entire function and its linear differential polynomials

    Goutam Kumar Ghosh

    Abstract : In this paper, we study a uniqueness problem of entire functions that share two linear polynomials with its linear differential polynomial. We deduce two theorems which improve some previous results given by I. Lahiri [7].

  • 2022-04-30

    On the conformal triharmonic maps

    Seddik Ouakkas, Yasmina Reguig

    Abstract : In this paper, we give the necessary and sufficient condition for the conformal mapping $phi :left(mathbb{R}^{n},g_{0}ight)ightarrow left( N^{n},hight)$ ($n geq 3$) to be triharmonic where we prove that the gradient of its dilation is a solution of a fourth-order elliptic partial differential equation. We construct some examples of triharmonic maps which are not biharmonic and we calculate the trace of the stress-energy tensor associated with the triharmonic maps.

  • 2023-04-30

    Characterizations of (Jordan) derivations on Banach algebras with local actions

    Jiankui Li, Shan Li, Kaijia Luo

    Abstract : Let $\mathcal{A}$ be a unital Banach $*$-algebra and $\mathcal{M}$ be a unital $*$-$\mathcal{A}$-bimodule. If $W$ is a left separating point of $\mathcal{M}$, we show that every $*$-derivable mapping at $W$ is a Jordan derivation, and every $*$-left derivable mapping at $W$ is a Jordan left derivation under the condition $W \mathcal{A}=\mathcal{A}W$. Moreover we give a complete description of linear mappings $\delta$ and $\tau$ from $\mathcal{A}$ into $\mathcal{M}$ satisfying $\delta(A)B^*+A\tau(B)^*=0$ for any $A, B\in \mathcal{A}$ with $AB^*=0$ or $\delta(A)\circ B^*+A\circ\tau(B)^*=0$ for any $A, B\in \mathcal{A}$ with $A\circ B^*=0$, where $A\circ B=AB+BA$ is the Jordan product.

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October, 2023
Vol.38 No.4

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