Communications of the
Korean Mathematical Society
CKMS
ISSN(Print) 1225-1763
ISSN(Online) 2234-3024
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2023-01-31
Generalizing some Fibonacci--Lucas relations
Junghyun Hong, Jongmin Lee, Ho ParkAbstract : 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.
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2022-10-31
The independence and independent dominating numbers of the total graph of a finite commutative ring
Baha' Abughazaleh, Omar AbedRabbu AbughneimAbstract : 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.
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2023-04-30
Uniqueness of meromorphic function with its $k$-th derivative sharing two small functions under different weights
Abhijit Banerjee, Arpita KunduAbstract : 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.}.
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2022-07-31
Multi-derivations and some approximations
Abasalt Bodaghi, Hassan FeizabadiAbstract : 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.
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2022-04-30
Relationship between the structure of a quotient ring and the behavior of certain additive mappings
Karim Bouchannafa, Moulay Abdallah Idrissi, Lahcen OukhtiteAbstract : The principal aim of this paper is to study the connection between the structure of a quotient ring $R/P$ and the behavior of special additive mappings of $R.$ More precisely, we characterize the commutativity of $R/P$ using derivations (generalized derivations) of $R$ satisfying algebraic identities involving the prime ideal $P.$ Furthermore, we provide examples to show that the various restrictions imposed in the hypothesis of our theorems are not superfluous.
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2022-01-31
When is $C(X)$ an EM-ring?
Emad Abuosba, Isaaf AtassiAbstract : A commutative ring with unity $R$ is called an EM-ring if for any finitely generated ideal $I$ there exist $a$ in $R$ and a finitely generated ideal $J $ with $limfunc{Ann}(J)=0$ and $I=aJ$. In this article it is proved that $ C(X)$ is an EM-ring if and only if for each $Uin Cozleft( Xight) $, and each $gin C^{ast }left( Uight) $ there is $Vin Cozleft( Xight) $ such that $Usubseteq V$, $overline{V}=X$, and $g$ is continuously extendable on $V$. Such a space is called an EM-space. It is shown that EM-spaces include a large class of spaces as F-spaces and cozero complemented spaces. It is proved among other results that $X$ is an EM-space if and only if the Stone-v{C}ech compactification of $X$ is.
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2022-04-30
Coefficient estimates for functions associated with vertical strip domain
Serap BulutAbstract : In this paper, we consider a convex univalent function $f_{alpha ,eta }$ which maps the open unit disc $mathbb{U}$ onto the vertical strip domain egin{equation*} Omega _{alpha ,eta }=left{ win mathbb{C}:alpha
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2022-04-30
Global attractor for a semilinear strongly degenerate parabolic equation with exponential nonlinearity in unbounded domains
Nguyen Xuan TuAbstract : We study the existence and long-time behavior of weak solutions to a class of strongly degenerate semilinear parabolic equations with exponential nonlinearities on $mathbb R^N $. To overcome some significant difficulty caused by the lack of compactness of the embeddings, the existence of a global attractor is proved by combining the tail estimates method and the asymptotic {it a priori} estimate method.
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2022-01-31
Some fixed point theorems for weakly Picard operators in complete metric spaces and applications
Doan Trong Hieu, Bui The HungAbstract : In this paper, we prove new fixed point theorems for single-valued and multi-valued weakly Picard operators in complete metric linebreak spaces and give several examples. As applications, we give several results to Fredholm integral equation.
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2022-01-31
$b$-Generalized derivations on Banach algebras
Husain AlhazmiAbstract : In this paper, we show, among others, that if $A$ is a Banach algebra satisfying a functional identity involving a $b$-generalized derivation $F$ on $A$, under some mild conditions, is of the form $F(x)=ax$ for all $xin R$, where $ain Q_r$, a right Martindale quotient ring of $A$.
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A question about maximal non $\phi$-chained subrings
Atul Gaur, Rahul Kumar
Commun. Korean Math. Soc. 2023; 38(1): 11-19
https://doi.org/10.4134/CKMS.c210272 -
Directional convexity of combinations of harmonic half-plane and strip mappings
Subzar Beig, Vaithiyanathan Ravichandran
Commun. Korean Math. Soc. 2022; 37(1): 125-136
https://doi.org/10.4134/CKMS.c200470 -
Properties of functions with bounded rotation associated with lima\c{c}on class
Kanwal Jabeen, Afis Saliu
Commun. Korean Math. Soc. 2022; 37(4): 995-1007
https://doi.org/10.4134/CKMS.c210273 -
On the index and biderivations of simple Malcev algebras
Abdelaziz Ben Yahya, Said Boulmane
Commun. Korean Math. Soc. 2022; 37(2): 385-397
https://doi.org/10.4134/CKMS.c210156
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Results concerning semi-symmetric metric $F$-connections on the Hsu-$B$ manifolds
Uday Chand De, Aydin Gezer, Cagri Karaman
Commun. Korean Math. Soc. 2023; 38(3): 837-846
https://doi.org/10.4134/CKMS.c220031 -
Fractional integration and differentiation of the $(p,q)$--extended modified Bessel function of the second kind and integral transforms
Purnima Chopra, Mamta Gupta, Kanak Modi
Commun. Korean Math. Soc. 2023; 38(3): 755-772
https://doi.org/10.4134/CKMS.c220132 -
The $p$-part of divisor class numbers for cyclotomic function fields
Daisuke Shiomi
Commun. Korean Math. Soc. 2023; 38(3): 715-723
https://doi.org/10.4134/CKMS.c220271 -
Chen invariants and statistical submanifolds
Hitoshi Furuhata, Izumi Hasegawa, Naoto Satoh
Commun. Korean Math. Soc. 2022; 37(3): 851-864
https://doi.org/10.4134/CKMS.c210185
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