Communications of the
Korean Mathematical Society
CKMS
ISSN(Print) 1225-1763
ISSN(Online) 2234-3024
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2023-07-31
Results concerning semi-symmetric metric $F$-connections on the Hsu-$B$ manifolds
Uday Chand De, Aydin Gezer, Cagri KaramanAbstract : In this paper, we firstly construct a Hsu-$B$ manifold and give some basic results related to it. Then, we address a semi-symmetric metric $F$-connection on the Hsu-$B$ manifold and obtain the curvature tensor fields of such connection, and study properties of its curvature tensor and torsion tensor fields.
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2023-10-31
A variant of Wilson's functional equation on semigroups
YOUSSEF ASERRAR, ABDELLATIF CHAHBI, ELHOUCIEN ELQORACHIAbstract : Let $S$ be a semigroup. We determine the complex-valued solutions of the following functional equation \[f(xy)+\mu (y)f(\sigma (y)x) = 2f(x)g(y),\ x,y\in S,\] where $\sigma:S\rightarrow S$ is an automorphism, and $\mu :S\rightarrow \mathbb{C}$ is a multiplicative function such that $\mu (x\sigma (x))=1$ for all $x\in S$.
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2023-10-31
Joint essential numerical spectrum and Jeribi essential numerical spectrum of linear operators in Banach spaces
Bouthaina Abdelhedi, Wissal Boubaker, Nedra MoallaAbstract : The purpose of this paper is to introduce the concept of joint essential numerical spectrum $\sigma_{en}(\cdot)$ of $q$-tuple of operators on a Banach space and to study its properties. This notion generalize the notion of the joint essential numerical range.
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2023-07-31
Areas of polygons with vertices from Lucas sequences on a plane
SeokJun Hong, SiHyun Moon, Ho Park, SeoYeon Park, SoYoung SeoAbstract : Area problems for triangles and polygons whose vertices have Fibonacci numbers on a plane were presented by A. Shriki, O. Liba, and S. Edwards et al. In 2017, V. P. Johnson and C. K. Cook addressed problems of the areas of triangles and polygons whose vertices have various sequences. This paper examines the conditions of triangles and polygons whose vertices have Lucas sequences and presents a formula for their areas.
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2023-10-31
Analytic functions with conic domains associated with certain generalized $q$-integral operator
OM P. AHUJA, Asena \c{C}etinkaya, NAVEEN KUMAR JAINAbstract : In this paper, we define a new subclass of $k$-uniformly starlike functions of order $\gamma~ (0\leq\gamma<1)$ by using certain generalized $q$-integral operator. We explore geometric interpretation of the functions in this class by connecting it with conic domains. We also investigate $q$-sufficient coefficient condition, $q$-Fekete-Szeg\"{o} inequalities, $q$-Bieberbach-De Branges type coefficient estimates and radius problem for functions in this class. We conclude this paper by introducing an analogous subclass of $k$-uniformly convex functions of order $\gamma$ by using the generalized $q$-integral operator. We omit the results for this new class because they can be directly translated from the corresponding results of our main class.
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2023-10-31
Transversal lightlike submersions from indefinite Sasakian manifolds onto lightlike manifolds
Shiv Sharma Shukla, Vipul SinghAbstract : In this paper, we introduce and study two new classes of lightlike submersions, called radical transversal and transversal lightlike submersions between an indefinite Sasakian manifold and a lightlike manifold. We give examples and investigate the geometry of distributions involved in the definitions of these lightlike submersions. We also study radical transversal and transversal lightlike submersions from an indefinite Sasakian manifold onto a lightlike manifold with totally contact umbilical fibers.
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2023-07-31
Generic lightlike submanifolds of semi-Riemannian product manifolds
Nand Kishor Jha, Jatinder Kaur, Sangeet Kumar, Megha PruthiAbstract : We introduce the study of generic lightlike submanifolds of a semi-Riemannian product manifold. We establish a characterization theorem for the induced connection on a generic lightlike submanifold to be a metric connection. We also find some conditions for the integrability of the distributions associated with generic lightlike submanifolds and discuss the geometry of foliations. Then we search for some results enabling a generic lightlike submanifold of a semi-Riemannian product manifold to be a generic lightlike product manifold. Finally, we examine minimal generic lightlike submanifolds of a semi-Riemannian product manifold.
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2023-10-31
Equality in degrees of compactness: Schauder's theorem and $s$-numbers
Asuman Guven Aksoy, Daniel Akech ThiongAbstract : 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 $T^*$.
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2023-10-31
Approximately local derivations on $\ell^{1}$-Munn algebras with applications to semigroup algebras
Ahmad Alinejad, Morteza Essmaili, Hatam VahdatiAbstract : At the present paper, we investigate bounded approximately local derivations of $\ell^{1}$-Munn algebra ${\mathbb M}_{I}(\mathcal{A})$, where $I$ is an arbitrary non-empty set and $\mathcal A$ is an approximately locally unital Banach algebra. Indeed, we show that if ${_\mathcal A}B(\mathcal A ,{\mathcal A}^{\ast})$ and $B_{\mathcal A}(\mathcal A ,{\mathcal A}^{\ast})$ are reflexive, then every bounded approximately local derivation from ${\mathbb M}_{I}(\mathcal A)$ into any Banach ${\mathbb M}_{I}(\mathcal A)$-bimodule $ X$ is a derivation. Finally, we apply this result to study bounded approximately local derivations of the semigroup algebra $\ell^{1}(S)$, where $S$ is a uniformly locally finite inverse semigroup.
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2023-10-31
On graded $N$-irreducible ideals of commutative graded rings
Anass Assarrar, Najib MahdouAbstract : Let $R$ be a commutative graded ring with nonzero identity and $n$ a positive integer. Our principal aim in this paper is to introduce and study the notions of graded $n$-irreducible and strongly graded $n$-irreducible ideals which are generalizations of $n$-irreducible and strongly $n$-irreducible ideals to the context of graded rings, respectively. A proper graded ideal $I$ of $R$ is called graded $n$-irreducible (respectively, strongly graded $n$-irreducible) if for each graded ideals $I_{1}, \ldots,I_{n+1}$ of $R$, $I=I_{1} \cap \cdots \cap I_{n+1}$ (respectively, $I_{1} \cap \cdots \cap I_{n+1} \subseteq I$ ) implies that there are $n$ of the $I_{i}$ 's whose intersection is $I$ (respectively, whose intersection is in $I$). In order to give a graded study to this notions, we give the graded version of several other results, some of them are well known. Finally, as a special result, we give an example of a graded $n$-irreducible ideal which is not an $n$-irreducible ideal and an example of a graded ideal which is graded $n$-irreducible, but not graded $(n-1)$-irreducible.
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On partial sums of four parametric Wright function
Muhey U Din
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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 -
Note on the multifractal measures of Cartesian product sets
Najmeddine Attia, Rihab Guedri, Omrane Guizani
Commun. Korean Math. Soc. 2022; 37(4): 1073-1097
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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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Formulas and relations for Bernoulli-type numbers and polynomials derive from Bessel function
Selin Selen OZBEK SIMSEK, Yilmaz SIMSEK
Commun. Korean Math. Soc. 2023; 38(4): 1175-1189
https://doi.org/10.4134/CKMS.c230045 -
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 -
Miao-Tam equation on almost coK"{a}hler manifolds
Tarak Mandal
Commun. Korean Math. Soc. 2022; 37(3): 881-891
https://doi.org/10.4134/CKMS.c210225 -
Uniform distributions on curves and quantization
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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