Abstract : In the present paper, we have studied Miao-Tam equation on three dimensional almost coK"{a}hler manifolds. We have also proved that there does not exist non-trivial solution of Miao-Tam equation on the said manifolds if the dimension is greater than three. Also we give an example to verify the deduced results.
Abstract : In this work, we introduce a new subclass of analytic functions of complex order involving the $left( p,qight) $-derivative operator defined in the open unit disc. For this class, several Fekete-Szeg"{o} type coefficient inequalities are derived. We obtain the results of Srivastava extit{et al.~}cite{SR} as consequences of the main theorem in this study.
Abstract : In this paper, we introduce the multi-derivations on rings and present some examples of such derivations. Then, we unify the system of functional equations defining a multi-derivation to a single formula. Applying a fixed point theorem, we will establish the generalized Hyers--Ulam stability of multi-derivations in Banach module whose upper bounds are controlled by a general function. Moreover, we give some important applications of this result to obtain the known stability outcomes.
Abstract : 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.}.
Abstract : Edgar obtained an identity between Fibonacci and Lucas numbers which generalizes previous identities of Benjamin--Quinn and Marques. Recently, Dafnis provided an identity similar to Edgar's. In the present article we give some generalizations of Edgar's and Dafnis's identities.
Abstract : Let $C[0,T]$ denote an analogue of Weiner space, the space of real-valued continuous on $[0,T]$. In this paper, we investigate the translation of time interval $[0,T]$ defining the analogue of Winer space $C[0,T]$. As applications of the result, we derive various relationships between the analogue of Wiener space and its product spaces. Finally, we express the analogue of Wiener measures on $C[0,T]$ as the analogue of Wiener measures on $C[0,s]$ and $C[s,T]$ with $0
Abstract : 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 [7].
Abstract : 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.
Abstract : In this article, an alternating Fibonacci sequence is defined from a second-order linear homogeneous recurrence relation with constant coefficients. Then, the determinant, inverse, and eigenvalues of the circulant matrices with entries in the first row having the formation of the sequence are formulated explicitly in a simple way. In this study, the method for deriving the formulation of the determinant and inverse is simply using traditional elementary row or column operations. For the eigenvalues, the known formulation from the case of general circulant matrices is simplified by considering the specialty of the sequence and using cyclic group properties. We also propose algorithms for the formulation to show how efficient the computations are.
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.
Muhey U Din
Commun. Korean Math. Soc. 2022; 37(3): 681-692
https://doi.org/10.4134/CKMS.c200469
Traiwat Intarawong, Boonrod Yuttanan
Commun. Korean Math. Soc. 2023; 38(2): 355-364
https://doi.org/10.4134/CKMS.c220139
Najmeddine Attia, Rihab Guedri, Omrane Guizani
Commun. Korean Math. Soc. 2022; 37(4): 1073-1097
https://doi.org/10.4134/CKMS.c210350
Hitoshi Furuhata, Izumi Hasegawa, Naoto Satoh
Commun. Korean Math. Soc. 2022; 37(3): 851-864
https://doi.org/10.4134/CKMS.c210185
Selin Selen OZBEK SIMSEK, Yilmaz SIMSEK
Commun. Korean Math. Soc. 2023; 38(4): 1175-1189
https://doi.org/10.4134/CKMS.c230045
Hitoshi Furuhata, Izumi Hasegawa, Naoto Satoh
Commun. Korean Math. Soc. 2022; 37(3): 851-864
https://doi.org/10.4134/CKMS.c210185
Tarak Mandal
Commun. Korean Math. Soc. 2022; 37(3): 881-891
https://doi.org/10.4134/CKMS.c210225
Joseph Rosenblatt, Mrinal Kanti Roychowdhury
Commun. Korean Math. Soc. 2023; 38(2): 431-450
https://doi.org/10.4134/CKMS.c210434
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