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 $n=3$.
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.
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.
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.
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.
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.
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 .
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 $\theta=\frac{\pi}{4}.$
Abstract : In this paper, we give some sufficient conditions for an almost Hermitian manifold to be Kahler.
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.
Ismael Akray, Amin Mahamad Zebari
Commun. Korean Math. Soc. 2023; 38(1): 21-38
https://doi.org/10.4134/CKMS.c210349
Vinay Kumar, Rajendra Prasad, Sandeep Kumar Verma
Commun. Korean Math. Soc. 2023; 38(1): 205-221
https://doi.org/10.4134/CKMS.c210433
Ioannis Diamantis
Commun. Korean Math. Soc. 2022; 37(4): 1221-1248
https://doi.org/10.4134/CKMS.c210169
Harish Chandra, Anurag Kumar Patel
Commun. Korean Math. Soc. 2023; 38(2): 451-459
https://doi.org/10.4134/CKMS.c220108
Vinay Kumar, Rajendra Prasad, Sandeep Kumar Verma
Commun. Korean Math. Soc. 2023; 38(1): 205-221
https://doi.org/10.4134/CKMS.c210433
Ismael Akray, Amin Mahamad Zebari
Commun. Korean Math. Soc. 2023; 38(1): 21-38
https://doi.org/10.4134/CKMS.c210349
Anjan Kumar Bhuniya, Manas Kumbhakar
Commun. Korean Math. Soc. 2023; 38(1): 1-9
https://doi.org/10.4134/CKMS.c210057
Traiwat Intarawong, Boonrod Yuttanan
Commun. Korean Math. Soc. 2023; 38(2): 355-364
https://doi.org/10.4134/CKMS.c220139
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