Communications of the
Korean Mathematical Society
CKMS
ISSN(Print) 1225-1763
ISSN(Online) 2234-3024
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2022-04-30
A note on discrete semigroups of bounded linear operators on non-archimedean Banach spaces
Aziz Blali, Abdelkhalek El Amrani, Jawad EttaybAbstract : Let $Ain B(X)$ be a spectral operator on a non-archimedean Banach space over an algebraically closed field. In this note, we give a necessary and sufficient condition on the resolvent of $A$ so that the discrete semigroup consisting of powers of $A$ is uniformly-bounded.
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2022-10-31
Note on the multifractal measures of Cartesian product sets
Najmeddine Attia, Rihab Guedri, Omrane GuizaniAbstract : In this paper, we shall be concerned with evaluation of multifractal Hausdorff measure ${\mathcal H}^{q,t}_\mu$ and multifractal packing measure ${\mathcal P}^{q,t}_\mu$ of Cartesian product sets by means of the measure of their components. This is done by investigating the density result introduced in \cite{Olsen95}. As a consequence, we get the inequalities related to the multifractal dimension functions, proved in \cite{Olsen96}, by using a unified method for all the inequalities. Finally, we discuss the extension of our approach to studying the multifractal Hewitt-Stromberg measures of Cartesian product sets.
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2023-01-31
A question about maximal non $\phi$-chained subrings
Atul Gaur, Rahul KumarAbstract : Let $\mathcal{H}_0$ be the set of rings $R$ such that $Nil(R) = Z(R)$ is a divided prime ideal of $R$. The concept of maximal non $\phi$-chained subrings is a generalization of maximal non valuation subrings from domains to rings in $\mathcal{H}_0$. This generalization was introduced in \cite{rahul} where the authors proved that if $R \in \mathcal{H}_0$ is an integrally closed ring with finite Krull dimension, then $R$ is a maximal non $\phi$-chained subring of $T(R)$ if and only if $R$ is not local and $|[R, T(R)]|$ = $\dim (R) + 3$. This motivates us to investigate the other natural numbers $n$ for which $R$ is a maximal non $\phi$-chained subring of some overring $S$. The existence of such an overring $S$ of $R$ is shown for $3\leq n \leq 6$, and no such overring exists for $n = 7$.
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2022-01-31
Directional convexity of combinations of harmonic half-plane and strip mappings
Subzar Beig, Vaithiyanathan RavichandranAbstract : For $k=1,2$, let $f_k=h_k+overline{g_k}$ be normalized harmonic right half-plane or vertical strip mappings. We consider the convex combination $hat{f}=eta f_1+(1-eta)f_2 =eta h_1+(1-eta)h_2 +overline{overline{eta} g_1+(1-overline{eta})g_2}$ and the combination $ ilde{f}=eta h_1+(1-eta)h_2+overline{eta g_1+(1-eta)g_2}$. For real $eta$, the two mappings $hat{f}$ and $ ilde{f}$ are the same. We investigate the univalence and directional convexity of $hat{f}$ and $ ilde{f}$ for $etainmathbb{C}$. Some sufficient conditions are found for convexity of the combination $ ilde{f}$.
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2022-10-31
Properties of functions with bounded rotation associated with lima\c{c}on class
Kanwal Jabeen, Afis SaliuAbstract : In this article, we initiate subclasses of functions with boundary and radius rotations that are related to lima\c{c}on domains and examine some of their geometric properties. Radius results associated with functions in these classes and their linear combination are studied. Furthermore, the growth rate of coefficients, arc length and coefficient estimates are derived for these novel classes. Overall, some useful consequences of our findings are also illustrated.
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2022-04-30
On the index and biderivations of simple Malcev algebras
Abdelaziz Ben Yahya, Said BoulmaneAbstract : Let $(M,[;,;])$ be a finite dimensional Malcev algebra over an algebraically closed field $mathbb{F}$ of characteristic 0. We first prove that, $(M,[;,;])$ (with $[M,M] eq 0$) is simple if and only if $ind(M)=1$ (i.e., $M$ admits a unique (up to a scalar multiple) invariant scalar product). Further, we characterize the form of skew-symmetric biderivations on simple Malcev algebras. In particular, we prove that the simple seven dimensional non-Lie Malcev algebra has no nontrivial skew-symmetric biderivation.
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2023-01-31
Functions subordinate to the exponential function
Priya G. Krishnan, Vaithiyanathan Ravichandran, Ponnaiah SaikrishnanAbstract : We use the theory of differential subordination to explore various inequalities that are satisfied by an analytic function $p$ defined on the unit disc so that the function $p$ is subordinate to the function $e^z$. These results are applied to find sufficient conditions for the normalised analytic functions $f$ defined on the unit disc to satisfy the subordination $zf'(z)/f(z) \prec e^z$.
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2022-07-31
Chen invariants and statistical submanifolds
Hitoshi Furuhata, Izumi Hasegawa, Naoto SatohAbstract : We define a kind of sectional curvature and $delta$-invariants for statistical manifolds. For statistical submanifolds the sum of the squared mean curvature and the squared dual mean curvature is bounded below by using the $delta$-invariant. This inequality can be considered as a generalization of the so-called Chen inequality for Riemannian submanifolds.
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2022-01-31
Infinitely many homoclinic solutions for different classes of fourth-order differential equations
Mohsen TimoumiAbstract : In this article, we study the existence and multiplicity of homoclinic solutions for the following fourth-order differential equation $$u^{(4)}(x)+omega u''(x)+a(x)u(x)=f(x,u(x)), forall xinmathbb{R} leqno(1)$$ where $a(x)$ is not required to be either positive or coercive, and $F(x,u)=int^{u}_{0}f(x,v)dv$ is of subquadratic or superquadratic growth as $left|uight|ightarrowinfty$, or satisfies only local conditions near the origin (i.e., it can be subquadratic, superquadratic or asymptotically quadratic as $|u|ightarrowinfty$). To the best of our knowledge, there is no result published concerning the existence and multiplicity of homoclinic solutions for (1) with our conditions. The proof is based on variational methods and critical point theory.
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2022-07-31
Some results on the geometry of a non-conformal deformation of a metric
Nour Elhouda Djaa, Abderrahim ZaganeAbstract : Let $(M^{m},g)$ be an $m$-dimensional Riemannian manifold. In this paper, we introduce a new class of metric on $(M^{m},g)$, obtained by a non-conformal deformation of the metric $g$. First we investigate the Levi-Civita connection of this metric. Secondly we characterize the Riemannian curvature, the sectional curvature and the scalar curvature. In the last section we characterizes some class of proper biharmonic maps. Examples of proper biharmonic maps are constructed when $(M^{m}, g)$ is an Euclidean space.
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Jordan $\mathcal{G}_n$-derivations on path algebras
Abderrahim Adrabi, Driss Bennis, Brahim Fahid
Commun. Korean Math. Soc. 2022; 37(4): 957-967
https://doi.org/10.4134/CKMS.c210346 -
Generalized Padovan sequences
Jhon J. Bravo, Jose L. Herrera
Commun. Korean Math. Soc. 2022; 37(4): 977-988
https://doi.org/10.4134/CKMS.c210367 -
On partial sums of four parametric Wright function
Muhey U Din
Commun. Korean Math. Soc. 2022; 37(3): 681-692
https://doi.org/10.4134/CKMS.c200469 -
On a first order strong differential subordination and application to univalent functions
Rasoul Aghalary, Parviz Arjomandinia
Commun. Korean Math. Soc. 2022; 37(2): 445-454
https://doi.org/10.4134/CKMS.c210070
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Hyers-Ulam stability of fractional stochastic differential equations with random impulse
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 -
Unitary analogues of a generalized number-theoretic sum
Traiwat Intarawong, Boonrod Yuttanan
Commun. Korean Math. Soc. 2023; 38(2): 355-364
https://doi.org/10.4134/CKMS.c220139 -
The dimension graph for modules over commutative rings
Shiroyeh Payrovi
Commun. Korean Math. Soc. 2023; 38(3): 733-740
https://doi.org/10.4134/CKMS.c220273 -
On nonnil-SFT rings
Ali Benhissi, Abdelamir Dabbabi
Commun. Korean Math. Soc. 2023; 38(3): 663-677
https://doi.org/10.4134/CKMS.c220230
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