Abstract : In this paper, a new subclass, $\mathcal{SC}_{\sigma}^{\mu,{p},{q}}({r},{s};x)$, of Sakaguchi-type analytic bi-univalent functions defined by $({p},{q})$-derivative operator using Horadam polynomials is constructed and investigated. The initial coefficient bounds for $|a_{2}|$ and $|a_{3}|$ are obtained. Fekete-Szeg\"{o} inequalities for the class are found. Finally, we give some corollaries.
Abstract : Bennis and El Hajoui have defined a (commutative unital) ring $R$ to be $S$-coherent if each finitely generated ideal of $R$ is a $S$-finitely presented $R$-module. Any coherent ring is an $S$-coherent ring. Several examples of $S$-coherent rings that are not coherent rings are obtained as byproducts of our study of the transfer of the $S$-coherent property to trivial ring extensions and amalgamated duplications.
Abstract : Let ${\mathcal B}(H)$ be the algebra of all bounded linear operators on a Hilbert space $H$ with $\operatorname{dim} (H)>2$. Let ${\mathcal{G} \mathcal{P}}$ be the subset of ${\mathcal B}(H)$ of all generalized projection operators. In this paper, we give a complete characterization of surjective maps $\Phi: {\mathcal B}(H) \rightarrow {\mathcal B}(H)$ satisfying $A-\lambda B \in {\mathcal{G} \mathcal{P}} \Leftrightarrow \Phi(A)-\lambda \Phi(B) \in {\mathcal{G} \mathcal{P}}$ for any $A, B \in {\mathcal B}(H)$ and $\lambda \in \mathbb{C}$.
Abstract : In 2019, Mathur and Solanki \cite{7,8} obtained a few transformation formulas for Appell, Horn and the Kamp\'{e} de F\'{e}riet functions. Unfortunately, some of the results are well-known and very old results in literature while others are erroneous. Thus the aim of this note is to provide the results in corrected forms and some of the results have been written in more compact form.
Abstract : An (additive) commutative monoid is called atomic if every given non-invertible element can be written as a sum of atoms (i.e., irreducible elements), in which case, such a sum is called a factorization of the given element. The number of atoms (counting repetitions) in the corresponding sum is called the length of the factorization. Following Geroldinger and Zhong, we say that an atomic monoid $M$ is a length-finite factorization monoid if each $b \in M$ has only finitely many factorizations of any prescribed length. An additive submonoid of $\mathbb{R}_{\ge 0}$ is called a positive monoid. Factorizations in positive monoids have been actively studied in recent years. The main purpose of this paper is to give a better understanding of the non-unique factorization phenomenon in positive monoids through the lens of the length-finite factorization property. To do so, we identify a large class of positive monoids which satisfy the length-finite factorization property. Then we compare the length-finite factorization property to the bounded and the finite factorization properties, which are two properties that have been systematically investigated for more than thirty years.
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 $T^*$.
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.
Abstract : Let $\mathcal{R}$ be a $\sigma$-prime ring with involution $\sigma$. The main \linebreak objective of this paper is to describe the structure of the $\sigma$-prime ring $\mathcal{R}$ with involution $\sigma$ satisfying certain differential identities involving three derivations $\psi_1, \psi_2$ and $\psi_3$ such that $\psi_1[t_1,\sigma(t_1)]+[\psi_2(t_1),\psi_2(\sigma(t_1))] + [\psi_3(t_1),\sigma(t_1)]\in \mathcal{J}_Z$ for all $t_1\in \mathcal{R}$. Further, some other related results have also been discussed.
Abstract : In this paper, the concept of a maximal chain of ideals is introduced. Some properties of such chains are studied. We introduce some other concepts related to a maximal chain of ideals such as the $n$-maximal ideal, the maximal dimension of a ring $S$ $(M.\dim(S))$, the maximal depth of an ideal $K$ of $S$ $(M.d(K))$ and maximal height of an ideal $K(M.d(K))$.
Abstract : Let $X$ be a simply connected rationally elliptic space such that $H^{2}(X; {\mathbb Q})\neq0$. In this paper, we show that if $ H^{2n}(X^{[2n-2]}; {\mathbb Q})=0$ or if $\pi_{2n}(X^{2n}) \otimes {\mathbb Q}=0$ for all $n$, then $X$ is an $F_{0}$-space.
Dumitru Baleanu, Banupriya Kandasamy, Ramkumar Kasinathan, Ravikumar Kasinathan, Varshini Sandrasekaran
Commun. Korean Math. Soc. 2023; 38(3): 967-982
https://doi.org/10.4134/CKMS.c220231
Abhijit Banerjee, Arpita Kundu
Commun. Korean Math. Soc. 2023; 38(2): 525-545
https://doi.org/10.4134/CKMS.c220168
Sugi Guritman
Commun. Korean Math. Soc. 2023; 38(2): 341-354
https://doi.org/10.4134/CKMS.c220110
Tamem Al-Shorman, Malik Bataineh, Ece Yetkin Celikel
Commun. Korean Math. Soc. 2023; 38(2): 365-376
https://doi.org/10.4134/CKMS.c220169
Selin Selen OZBEK SIMSEK, Yilmaz SIMSEK
Commun. Korean Math. Soc. 2023; 38(4): 1175-1189
https://doi.org/10.4134/CKMS.c230045
Abdelhadi Zaim
Commun. Korean Math. Soc. 2023; 38(4): 1309-1320
https://doi.org/10.4134/CKMS.c230014
Shiv Sharma Shukla, Vipul Singh
Commun. Korean Math. Soc. 2023; 38(4): 1191-1213
https://doi.org/10.4134/CKMS.c220309
SHINE LAL ENOSE, RAMYA PERUMAL, PRASAD THANKARAJAN
Commun. Korean Math. Soc. 2023; 38(4): 1075-1090
https://doi.org/10.4134/CKMS.c220355
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