Abstract : In this paper, we study new classes of operators $k$-quasi $(m, n)$-paranormal operator, $k$-quasi $(m, n)^*$-paranormal operator, $k$-qu\-asi $(m, n)$-class~ $\mathcal{Q}$ operator and $k$-quasi $(m, n)$-class~ $\mathcal{Q^{*}}$ operator which are the generalization of $(m, n)$-paranormal and $(m, n)^*$-paranormal operators. We give matrix characterizations for $k$-quasi $(m, n)$-paranormal and $k$-quasi $(m, n)^*$-paranormal operators. Also we study some properties of $k$-quasi $(m, n)$-class~ $\mathcal{Q}$ operator and $k$-quasi $(m, n)$-class~ $\mathcal{Q}^*$ operators. Moreover, these classes of composition operators on $L^2$ spaces are characterized.
Abstract : Let $R$ be a commutative ring with identity. If the nilpotent radical $Nil(R)$ of $R$ is a divided prime ideal, then $R$ is called a $\phi$-ring. Let $R$ be a $\phi$-ring and $S$ be a multiplicative subset of $R$. In this paper, we introduce and study the class of nonnil-$S$-coherent rings, i.e., the rings in which all finitely generated nonnil ideals are $S$-finitely presented. Also, we define the concept of $\phi$-$S$-coherent rings. Among other results, we investigate the $S$-version of Chase's result and Chase Theorem characterization of nonnil-coherent rings. We next study the possible transfer of the nonnil-$S$-coherent ring property in the amalgamated algebra along an ideal and the trivial ring extension.
Abstract : In this erratum, we correct a mistake in the proof of Proposition 2.7. In fact the equivalence $(3)\Longleftarrow (4)$ ``$R$ is a quasi-regular ring if and only if $R$ is a reduced ring and every principal ideal contained in $Z(R)$ is a 0-ideal'' does not hold as we only have $Rx\subseteq O(S)$.
Abstract : Parallel conics have interesting area and chord properties. In this paper, we study such properties of conics and conic hypersurfaces. First of all, we characterize conics in the plane with respect to the above mentioned properties. Finally, we establish some characterizations of hypersurfaces with centrally symmetric hyperplane sections.
Abstract : Special examples of harmonic manifolds that are not symmetric, proving that the conjecture posed by Lichnerowicz fails in the non-compact case have been intensively studied. We completely classify homogeneous structures on Damek-Ricci spaces equipped with the left invariant metric.
Abstract : The present article contains the study of $D$-homothetically deformed $f$-Kenmotsu manifolds. Some fundamental results on the deformed spaces have been deduced. Some basic properties of the Riemannian metric as an inner product on both the original and deformed spaces have been established. Finally, applying the obtained results, soliton functions, Ricci curvatures and scalar curvatures of almost Riemann solitons with several kinds of potential vector fields on the deformed spaces have been characterized.
Abstract : Following the new description of an oriented full transformation on a finite chain given recently by Higgins and Vernitski in [4], in this short note we present a refinement of this description which is extendable to partial transformations and to injective partial transformations.
Abstract : We characterize metrizability and submetrizability for point-open, open-point and bi-point-open topologies on scalebox{0.98}{$C(X,Y)$}, where scalebox{0.98}{$C(X,Y)$} denotes the set of all continuous functions from space $X$ to $Y$; $X$ is a completely regular space and $Y$ is a locally convex space.
Abstract : In this paper, we extend the medial triangle theorem and Varignon's theorem to generic two-dimensional polygons and highlight the role played by diagonals in this process. One of the results is a synthetic definition of the concept of median for an $n$-sided polygon.
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.
Somya Malik, Vaithiyanathan Ravichandran
Commun. Korean Math. Soc. 2022; 37(4): 1025-1039
https://doi.org/10.4134/CKMS.c210322
Shaymaa S. Essa, Husam Q. Mohammad
Commun. Korean Math. Soc. 2023; 38(1): 55-67
https://doi.org/10.4134/CKMS.c210427
Gemechis File Duressa, Tariku Birabasa Mekonnen
Commun. Korean Math. Soc. 2023; 38(1): 299-318
https://doi.org/10.4134/CKMS.c220020
Zied Douzi, Bilel Selmi, Haythem Zyoudi
Commun. Korean Math. Soc. 2023; 38(2): 491-507
https://doi.org/10.4134/CKMS.c220154
Mircea Crasmareanu
Commun. Korean Math. Soc. 2023; 38(4): 1261-1269
https://doi.org/10.4134/CKMS.c230024
Urmila Biswas, Avijit Sarkar
Commun. Korean Math. Soc. 2023; 38(4): 1215-1231
https://doi.org/10.4134/CKMS.c220366
Ponmana Selvan Arumugam, Ganapathy Gandhi, Saravanan Murugesan, Veerasivaji Ramachandran
Commun. Korean Math. Soc. 2023; 38(4): 1163-1173
https://doi.org/10.4134/CKMS.c230034
Hanane AHARSSI, Kamal CHARRABI, Abdellah MAMOUNI
Commun. Korean Math. Soc. 2024; 39(1): 79-91
https://doi.org/10.4134/CKMS.c230128
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