Communications of the
Korean Mathematical Society
CKMS

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

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  • 2023-04-30

    A simple proof for a result on $n$-Jordan homomorphisms

    Choonkil Park, Abbas Zivari-Kazempour

    Abstract : In this short note, we give a simple proof of the main theorem of \cite{Cheshmavar} which states that every $n$-Jordan homomorphism $h:A\longrightarrow B$ between two commutative algebras $A$ and $B$ is an $n$-homomorphism.

  • 2022-04-30

    A fundamental theorem of calculus for the $M_{alpha}$-integral

    Abraham Perral Racca

    Abstract : This paper presents a fundamental theorem of calculus, an integration by parts formula and a version of equiintegrability convergence theorem for the $M_{alpha}$-integral using the $M_{alpha}$-strong Lusin condition. In the convergence theorem, to be able to relax the condition of being point-wise convergent everywhere to point-wise convergent almost everywhere, the uniform $M_{alpha}$-strong Lusin condition was imposed.

  • 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.

  • 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

    A note on generalizations of Bailey's identity involving products of generalized hypergeometric series

    Adem Kilicman, Shantha Kumari Kurumujji, Arjun K. Rathie

    Abstract : In the theory of hypergeometric and generalized hypergeometric series, the well-known and very useful identity due to Bailey (which is a generalization of the Preece's identity) plays an important role. The aim of this research paper is to provide generalizations of Bailey's identity involving products of generalized hypergeometric series in the most general form. A few known, as well as new results, have also been obtained as special cases of our main findings.

  • 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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  • 2022-04-30

    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.

  • 2023-10-31

    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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  • 2023-04-30

    Estimates for certain shifted convolution sums involving Hecke eigenvalues

    Guodong Hua

    Abstract : In this paper, we obtain certain estimates for averages of shifted convolution sums involving Hecke eigenvalues of classical holomorphic cusp forms. This generalizes some results of L\"{u} and Wang in this direction.

  • 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.

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January, 2024
Vol.39 No.1

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