Communications of the
Korean Mathematical Society
CKMS
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 KumarAbstract : 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.
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2023-04-30
Maximal chain of ideals and $n$-maximal ideal
Hemin A. Ahmad, Parween A. HummadiAbstract : 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 $K(M.d(K))$.
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2022-10-31
On strong exponential limit shadowing property
Ali DarabiAbstract : 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 LeAbstract : 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.
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2022-07-31
Study of gradient solitons in three dimensional Riemannian manifolds
Gour Gopal Biswas, Uday Chand DeAbstract : 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. SoenjayaAbstract : 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.
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2022-01-31
Toeplitz and Hankel operators with Carleson measure symbols
Jaehui ParkAbstract : 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.
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2023-04-30
Two linear polynomials shared by an entire function and its linear differential polynomials
Goutam Kumar GhoshAbstract : 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].
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2022-04-30
On the conformal triharmonic maps
Seddik Ouakkas, Yasmina ReguigAbstract : 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.
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2023-04-30
Characterizations of (Jordan) derivations on Banach algebras with local actions
Jiankui Li, Shan Li, Kaijia LuoAbstract : 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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Yamabe and Riemann solitons on Lorentzian para-Sasakian manifolds
Shruthi Chidananda, Venkatesha Venkatesha
Commun. Korean Math. Soc. 2022; 37(1): 213-228
https://doi.org/10.4134/CKMS.c200365 -
Some functional identities arising from derivations
Abdellah Mamouni, Lahcen Oukhtite, Mohammed Zerra
Commun. Korean Math. Soc. 2023; 38(1): 79-87
https://doi.org/10.4134/CKMS.c220004 -
Miao-Tam equation on almost coK"{a}hler manifolds
Tarak Mandal
Commun. Korean Math. Soc. 2022; 37(3): 881-891
https://doi.org/10.4134/CKMS.c210225 -
Sharp coefficient inequalities for certain subclasses of bi-univalent Bazileviv{c} functions
Amol Bhausaheb Patil
Commun. Korean Math. Soc. 2022; 37(1): 113-123
https://doi.org/10.4134/CKMS.c200468
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The measurability of Hewitt-Stromberg measures and dimensions
Zied Douzi, Bilel Selmi, Haythem Zyoudi
Commun. Korean Math. Soc. 2023; 38(2): 491-507
https://doi.org/10.4134/CKMS.c220154 -
Geometric properties on $(j,k)$-symmetric functions related to starlike and convex function
Priyabrat Gochhayat, Anuja Prajapati
Commun. Korean Math. Soc. 2022; 37(2): 455-472
https://doi.org/10.4134/CKMS.c210072 -
Existence and nonexistence of solutions for a class of Hamiltonian strongly degenerate elliptic system
Nguyen Viet Tuan
Commun. Korean Math. Soc. 2023; 38(3): 741-754
https://doi.org/10.4134/CKMS.c220080 -
Generalized Padovan sequences
Jhon J. Bravo, Jose L. Herrera
Commun. Korean Math. Soc. 2022; 37(4): 977-988
https://doi.org/10.4134/CKMS.c210367
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