Communications of the
Korean Mathematical Society

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

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  • Online first article July 11, 2024

    A variant of d'Alembert's and Wilson's functional equations for matrix valued functions

    Abdellatif Chahbi, Mohamed Chakiri, and Elhoucien ELqorachi

    Abstract : Given $M$ a monoid with a neutral element $e$ and $I_{n}$ the unit matrix of $\mathcal{M}_{n}(\mathbb{C})$. We show that the solutions of d'Alembert's functional equation for $n\times n$ matrices \begin{equation*} \left\lbrace\begin{array}{ll} \Phi(pr,qs)+\Phi(sp,rq)=2\Phi(p,q)\Phi(r,s),\quad p,q,r,s\in M,\\ \Phi(e,e)=I_{n}, \end{array}\right. \end{equation*} and a n-dimensional mixed vector-matrix Wilson's functional equation \begin{equation*} \left\lbrace\begin{array}{ll} f(pr,qs)+f(sp,rq)=2\Phi(r,s)f(p,q),\\ \Phi(p,q)=\Phi(q,p),\quad p,q,r,s\in M \end{array}\right. \end{equation*} are abelian. As an application, we solve the first functional equation on groups for the particular case of $n=3$.

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  • Online first article July 12, 2024

    Toeplitz Determinants for Lambda-Pseudo-Starlike Functions

    Murat Caglar, Ismaila O. Ibrahim, Timilehin Gideon Shaba, and Abbas Kareem Wanas

    Abstract : In this article, by making use of th eLambda-pseudo-starlike Functions, we introduce a certain family of normalized analytic functions in the open unit disk U and we establish coefficient estimates for the first four determinants of the Toeplitz matrices T2(2), T2(3), T3(2) and T3(1) for the functions belonging to this family. Further, some known and new results which follow as special cases of our results are also mentioned.

  • Online first article July 11, 2024

    On H_2-proper timelike hypersurfaces in Lorentz 4-space forms

    Firooz Pashaie

    Abstract : The ordinary mean curvature vector field $\bH$ on a submanifold $M$ of a space form is said to be {\it proper} if it satisfies equality $\Delta\bH=a\bH$ for a constant real number $a$. It is proven that every hypersurface of an Riemannian space form with proper mean curvature vector field has constant mean curvature. In this manuscript, we study the Lorentzian hypersurfaces with proper second mean curvature vector field of four dimensional Lorentzian space forms. We show that the scalar curvature of such a hypersurface has to be constant. In addition, as a classification result, we show that each Lorentzian hypersurface of a Lorentzian 4-space form with proper second mean curvature vector field is $\C$-biharmonic, $\C$-1-type or $\C$-null-2-type. Also, we prove that every $\bH_2$-proper Lorentzian hypersurface with constant ordinary mean curvature in a Lorentz 4-space form is 1-minimal.

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  • Online first article July 12, 2024

    The Chow ring of a sequence of point blow-ups

    Daniel Camazón Portela

    Abstract : Given a sequence of point blow-ups of smooth n−dimensional projective varieties Zi defined over an algebraically closed field k, Zs → Zs−1 → · · · → Z1 → Z0, we give two presentations of the Chow ring A•(Zs) of its sky. The first one using the classes of the total transforms of the exceptional components as generators and the second one using the classes of the strict transforms ones. We prove that the skies of two sequences of point blow-ups of the same length have isomorphic Chow rings. Finally we give a characterization of final divisor of a sequence of point blow-ups in terms of some relations defined over the Chow group of zero-cycles A0(Zs) of its sky.

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  • Online first article July 12, 2024

    Multivalent Non-Carath\'eodory Functions Involving Higher Order Derivatives

    Daniel Breaz, Kadhavoor Ragavan Karthikeyan, Sakkarai Lakshmi, and Alagiriswamy Senguttuvan

    Abstract : In this paper, we use higher order derivatives with regard to symmetric points to introduce a class of multivalent starlike functions. The major deviation is that we define some differential characterizations that are subordinate to a function whose real part is not greater than zero. The primary outcomes of this study are initial coefficients and the Fekete-Szeg\H{o} inequality for functions falling under the given class. Also, we have obtained an interesting subordination results involving symmetric functions. The results obtained here extend or unify the various other well-known and new results.

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  • Online first article July 11, 2024

    Super and strong gamma H-compactness in Hereditary m-Spaces

    Ahmad Al-Omari and Takashi Noiri

    Abstract : Let (X, m, H) be a hereditary m-space and gamma : m -------> P(X)$ be an operation on m. A subset A of X is said to be gamma H-compact relative to X if for every cover { U_\alpha : \alpha \in \Delta \} of A by m-open sets of X, there exists a finite subset Delta_0 of Delta such that A \setminus \cup\{ \gamma(U_\alpha) : \alpha \in \Delta_0 \} in H. In this paper, we define and investigate two kinds of strong forms of gamma H-compact relative to X.

  • Online first article July 10, 2024


    Phool Miyan

    Abstract : Abstract: Let K be a ring. An additive map uo to u is called Jordan involution on K if (uo)o = u and (uv + vu)o = uovo + vouo ∀ u, v ∈ K . If Θ is a η−generalized derivation (non-zero) on K associated with a derivation Ω on K , then it is shown that Θ(u) = γu ∀ u ∈ K such that γ ∈ Ξ and γ2 = 1, whenever Θ possess [Θ(u), Θ(uo)] = [u, uo] ∀ u ∈ K .

  • Online first article July 10, 2024

    The norming set of a symmetric $n$-linear form on the plane with a rotated supremum norm for $n=3, 4, 5$

    Sung Guen Kim

    Abstract : Let $n\in \mathbb{N}, n\geq 2.$ An element $(x_1, \ldots, x_n)\in E^n$ is called a {\em norming point} of $T\in {\mathcal L}(^n E)$ if $\|x_1\|=\cdots=\|x_n\|=1$ and $|T(x_1, \ldots, x_n)|=\|T\|,$ where ${\mathcal L}(^n E)$ denotes the space of all continuous $n$-linear forms on $E.$ For $T\in {\mathcal L}(^n E),$ we define $$\qopname\relax o{Norm}(T)=\Big\{(x_1, \ldots, x_n)\in E^n: (x_1, \ldots, x_n)~\mbox{is a norming point of}~T\Big\}.$$ $\qopname\relax o{Norm}(T)$ is called the {\em norming set} of $T$. Let $0\leq \theta\leq \frac{\pi}{4}$ and $\ell^2_{{\infty}, \theta}=\mathbb{R}^2$ with the rotated supremum norm $$\|(x, y)\|_{({\infty}, \theta)}=\max\Big\{|x cos \theta+y sin \theta|,~ |x sin \theta-y cos \theta|\Big\}.$$ In this paper, we characterize the norming set of $T\in {\mathcal L}(^n \ell_{(\infty, \theta)}^2).$ Using this result, we completely describe the norming set of $T\in {\mathcal L}_s(^n \ell_{(\infty, \theta)}^2)$ for $n=3, 4, 5,$ where ${\mathcal L}_s(^n \ell_{(\infty, \theta)}^2)$ denotes the space of all continuous symmetric $n$-linear forms on $\ell_{(\infty, \theta)}^2.$ We generalizes the results from [9] for $n=3$ and $\theta=\frac{\pi}{4}.$

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  • Online first article July 12, 2024

    A theorem on almost Hermitian manifolds

    Jaeman Kim

    Abstract : In this paper, we give some sufficient conditions for an almost Hermitian manifold to be Kahler.

  • Online first article July 12, 2024

    Corrigendum on "Oriented transformations on a finite chain: another description" [Commun. Korean Math. Soc. 38 (2023), No. 3, pp. 725--731]

    Vítor H. Fernandes

    Abstract : In this note, we aim to correct some of the results presented in \cite{Fernandes:2023}. Namely, the statements of Proposition 2.1, Corollary 2.2, Corollary 2.3, Theorem 2.4 and Theorem 2.6, concerning only the monoids $OP_n$ and $POP_n$, have to exclude transformations of rank two. All other results of \cite{Fernandes:2023}, as well as those mentioned above but for the monoids $OR_n$ and $POR_n$, do not require correction.

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