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Warped product pseudo-slant submanifolds of a Kenmotsu manifold
Mohammad Shuaib 대한수학회 2023 대한수학회논문집 Vol.38 No.2
For a pseudo-slant submanifold of a Kenmotsu manifold, we have worked out conditions in terms its canonical structure tensors, $T$ and $F$, and its shape operator so that it reduces to a warped product submanifold.
Results associated with the Schwarz lemma on the boundary
Bulent Nafi Ornek 대한수학회 2023 대한수학회논문집 Vol.38 No.2
In this paper, some estimations will be given for the analytic functions belonging to the class $\mathcal{R}\left( \alpha \right) $. In these estimations, an upper bound and a lower bound will be determined for the first coefficient of the expansion of the analytic function $h(z)$ and the modulus of the angular derivative of the function $\frac{zh^{\prime }(z)}{ h(z)}$, respectively. Also, the relationship between the coefficients of the analytical function $h(z)$ and the derivative mentioned above will be shown.
Singular and Marcinkiewicz integral operators on product domains
Badriya Al-Azri,Ahmad Al-Salman 대한수학회 2023 대한수학회논문집 Vol.38 No.2
In this paper, we prove $L^{p}$ estimates of a class of singular integral operators on product domains along surfaces defined by mappings that are more general than polynomials and convex functions. We assume that the kernels are in $L(\log L)^{2}(\mathbb{S}^{n-1}\times \mathbb{S}^{m-1})$. Furthermore, we\ prove $L^{p}$ estimates of the related class of Marcinkiewicz integral operators. Our results extend as well as improve previously known results.
Gherici Beldjilali,Nour Oubbiche 대한수학회 2023 대한수학회논문집 Vol.38 No.2
The aim of this paper is two-fold. First, we study the Chinea-Gonzalez class $C_{12}$ of almost contact metric manifolds and we discuss some fundamental properties. We show there is a one-to-one correspondence between $C_{12}$ and K\"ahlerian structures. Secondly, we give some basic results for Riemannian curvature tensor of $C_{12}$-manifolds and then establish equivalent relations among $\varphi$-sectional curvature. Concrete examples are given.
Characterizations of (Jordan) derivations on Banach algebras with local actions
Jiankui Li,Shan Li,Kaijia Luo 대한수학회 2023 대한수학회논문집 Vol.38 No.2
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.
Abhijit Banerjee,Arpita Kundu 대한수학회 2023 대한수학회논문집 Vol.38 No.2
In the paper, we have exhaustively studied about the uniqueness of meromorphic function sharing two small functions with its $k$-th derivative as these types of results have never been studied earlier. We have obtained a series of results which will improve and extend some recent results of Banerjee-Maity \cite{Ban-Maity_Contemp.}.
Two linear polynomials shared by an entire function and its linear differential polynomials
Goutam Kumar Ghosh 대한수학회 2023 대한수학회논문집 Vol.38 No.2
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 \cite{5}.
On graded $J$-ideals over graded rings
Tamem Al-Shorman,Malik Bataineh,Ece Yetkin Celikel 대한수학회 2023 대한수학회논문집 Vol.38 No.2
The goal of this article is to present the graded $J$-ideals of $G$-graded rings which are extensions of $J$-ideals of commutative rings. A graded ideal $P$ of a $G$-graded ring $R$ is a graded $J$-ideal if whenever $x,y\in h(R)$, if $xy\in P$ and $x\not\in J(R)$, then $y\in P$, where $h(R)$ and $J(R)$ denote the set of all homogeneous elements and the Jacobson radical of $R$, respectively. Several characterizations and properties with supporting examples of the concept of graded $J$-ideals of graded rings are investigated.
Unitary analogues of a generalized number-theoretic sum
Traiwat Intarawong,Boonrod Yuttanan 대한수학회 2023 대한수학회논문집 Vol.38 No.2
In this paper, we investigate the sums of the elements in the finite set $\{x^{k}:1\leq x\leq\frac{n}{m},\gcd_u(x,n)=1\}$, where $k$, $m$ and $n$ are positive integers and $\gcd_u(x,n)$ is the unitary greatest common divisor of $x$ and $n$. Moreover, for some cases of $k$ and $m$, we can give the explicit formulae for the sums involving some well-known arithmetic functions.