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 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

    On the Characterization of $F_{0}$-spaces

    Mahmoud Benkhalifa

    Abstract : Let $X$ be a simply connected rationally elliptic space such that $H^{2}(X; {\mathbb Q})\neq0$. In this paper, we show that if $ H^{2n}(X^{[2n-2]}; {\mathbb Q})=0$ or if $\pi_{2n}(X^{2n}) \otimes {\mathbb Q}=0$ for all $n$, then $X$ is an $F_{0}$-space.

  • 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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  • 2022-07-31

    Infinitely many homoclinic solutions for damped vibration systems with locally defined potentials

    Wafa Selmi, Mohsen Timoumi

    Abstract : In this paper, we are concerned with the existence of infinitely many fast homoclinic solutions for the following damped vibration system $$ddot{u}(t)+q(t)dot{u}(t)-L(t)u(t)+ abla W(t,u(t))=0, forall tinmathbb{R}, leqno(1)$$ where $qin C(mathbb{R},mathbb{R})$, $Lin C(mathbb{R},mathbb{R}^{N^{2}})$ is a symmetric and positive definite matix-valued function and $Win C^{1}(mathbb{R} imesmathbb{R}^{N},mathbb{R})$. The novelty of this paper is that, assuming that $L$ is bounded from below unnecessarily coercive at infinity, and $W$ is only locally defined near the origin with respect to the second variable, we show that $(1)$ possesses infinitely many homoclinic solutions via a variant symmetric mountain pass theorem.

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  • 2023-10-31

    Equality in degrees of compactness: Schauder's theorem and $s$-numbers

    Asuman Guven Aksoy, Daniel Akech Thiong

    Abstract : We investigate an extension of Schauder's theorem by studying the relationship between various $s$-numbers of an operator $T$ and its adjoint $T^*$. We have three main results. First, we present a new proof that the approximation number of $T$ and $T^*$ are equal for compact operators. Second, for non-compact, bounded linear operators from $X$ to $Y$, we obtain a relationship between certain $s$-numbers of $T$ and $T^*$ under natural conditions on $X$ and $Y$. Lastly, for non-compact operators that are compact with respect to certain approximation schemes, we prove results for comparing the degree of compactness of $T$ with that of its adjoint $T^*$.

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  • 2023-01-31

    Geometric inequalities for warped products submanifolds in generalized complex space forms

    Mohd Aquib, Mohd Aslam, Michel Nguiffo Boyom, Mohammad Hasan Shahid

    Abstract : In this article, we derived Chen's inequality for warped product bi-slant submanifolds in generalized complex space forms using semi-symmetric metric connections and discuss the equality case of the inequality. Further, we discuss non-existence of such minimal immersion. We also provide various applications of the obtained inequalities.

  • 2022-10-31

    The independence and independent dominating numbers of the total graph of a finite commutative ring

    Baha' Abughazaleh, Omar AbedRabbu Abughneim

    Abstract : Let $R$ be a finite commutative ring with nonzero unity and let $Z(R)$ be the zero divisors of $R$. The total graph of $R$ is the graph whose vertices are the elements of $R$ and two distinct vertices $x,y\in R$ are adjacent if $x+y\in Z(R)$. The total graph of a ring $R$ is denoted by $\tau (R)$. The independence number of the graph $\tau (R)$ was found in \cite{Nazzal}. In this paper, we again find the independence number of $\tau (R)$ but in a different way. Also, we find the independent dominating number of $\tau (R)$ . Finally, we examine when the graph $\tau (R)$ is well-covered.

  • 2022-07-31

    Solitons of K"{A}hlerian Norden space-time manifolds

    Praveena Manjappa Mundalamane, Bagewadi Channabasappa Shanthappa, Mallannara Siddalingappa Siddesha

    Abstract : We study solitons of K"{a}hlerian Norden space-time manifolds and Bochner curvature tensor in almost pseudo symmetric K"{a}hlerian space-time manifolds. It is shown that the steady, expanding or shrinking solitons depend on different relations of energy density/isotropic pressure, the cosmological constant, and gravitational constant.

  • 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 $K(M.d(K))$.

  • 2022-07-31

    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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April, 2024
Vol.39 No.2

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