Communications of the
Korean Mathematical Society
CKMS
ISSN(Print) 1225-1763
ISSN(Online) 2234-3024
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2022-10-31
Liouville theorems for the multidimensional fractional Bessel operators
Vanesa Galli, Sandra Molina, Alejandro QuinteroAbstract : In this paper, we establish Liouville type theorems for the fractional powers of multidimensional Bessel operators extending the results given in \cite{GMQ18}. In order to do this, we consider the distributional point of view of fractional Bessel operators studied in \cite{Mo18}.
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2023-01-31
Geometric inequalities for warped products submanifolds in generalized complex space forms
Mohd Aquib, Mohd Aslam, Michel Nguiffo Boyom, Mohammad Hasan ShahidAbstract : In this article, we derived Chen's inequality for warped product bi-slant submanifolds in generalized complex space forms using semi-symmetric metric connections and discuss the equality case of the inequality. Further, we discuss non-existence of such minimal immersion. We also provide various applications of the obtained inequalities.
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2022-10-31
On strong exponential limit shadowing property
Ali DarabiAbstract : In this study, we show that the strong exponential limit shadowing property (SELmSP, for short), which has been recently introduced, exists on a neighborhood of a hyperbolic set of a diffeomorphism. We also prove that $\Omega$-stable diffeomorphisms and $\mathcal{\mathcal{L}}$-hyperbolic homeomorphisms have this type of shadowing property. By giving examples, it is shown that this type of shadowing is different from the other shadowings, and the chain transitivity and chain mixing are not necessary for it. Furthermore, we extend this type of shadowing property to positively expansive maps with the shadowing property.
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2024-01-31
The class of $p$-demicompact operators on lattice normed spaces
Imen Ferjani, Bilel KrichenAbstract : In the present paper, we introduce a new class of operators called $p$-demicompact operators between two lattice normed spaces $X$ and $Y$. We study the basic properties of this class. Precisely, we give some conditions under which a $p$-bounded operator be $p$-demicompact. Also, a sufficient condition is given, under which each $p$-demicompact operator has a modulus which is $p$-demicompact. Further, we put in place some properties of this class of operators on lattice normed spaces.
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2022-10-31
Certain image formulas of $(p,\nu)$--extended Gauss' hypergeometric function and related Jacobi transforms
Purnima Chopra, Mamta Gupta, Kanak ModiAbstract : Our aim is to establish certain image formulas of the $ (p,\nu)$--extended Gauss' hypergeometric function $F_{\,p,\nu}(a,b;c;z)$ by using Saigo's hypergeometric fractional calculus (integral and differential) operators. Corresponding assertions for the classical Riemann-Liouville(R-L) and Erd\'elyi-Kober(E-K) fractional integral and differential operators are deduced. All the results are represented in terms of the Hadamard product of the $ (p,\nu)$--extended Gauss's hypergeometric function $F_{\,p,\nu}(a,b;c;z)$ and Fox-Wright function $_{r}\Psi_{s}(z)$. We also established Jacobi and its particular assertions for the Gegenbauer and Legendre transforms of the $ (p,\nu)$--extended Gauss' hypergeometric function $F_{\,p,\nu}(a,b;c;z)$.
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2024-01-31
Skew brace enhancements and virtual links
Melody Chang, Sam NelsonAbstract : We use the structure of skew braces to enhance the biquandle counting invariant for virtual knots and links for finite biquandles defined from skew braces. We introduce two new invariants: a single-variable polynomial using skew brace ideals and a two-variable polynomial using the skew brace group structures. We provide examples to show that the new invariants are not determined by the counting invariant and hence are proper enhancements.
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2023-01-31
Representations of $C^{\ast}$-ternary rings
Arpit Kansal, Ajay Kumar, Vandana RajpalAbstract : It is proved that there is a one to one correspondence between representations of $C^{\ast}$-ternary ring $M$ and $C^{\ast}$-algebra $\mathcal{A}(M)$. We discuss primitive and modular ideals of a $C^{\ast}$-ternary ring and prove that a closed ideal $I$ is primitive or modular if and only if so is the ideal $\mathcal{A}(I)$ of $\mathcal{A}(M)$. We also show that a closed ideal in $M$ is primitive if and only if it is the kernel of some irreducible representation of $M$. Lastly, we obtain approximate identity characterization of strongly quasi-central $C^{\ast}$-ternary ring and the ideal structure of the TRO $ V\otimes^{\text{\rm tmin}} B$ for a $C^{\ast}$-algebra $B$.
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2024-04-30
Horadam polynomials for a new subclass of Sakaguchi-type bi-univalent functions defined by $({p},{q})$-derivative operator
Vanithakumari B
, SARAVANAN G , Baskaran S , Sibel Yalcin 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.
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2023-07-31
Square congruence graphs
J SURESH KUMAR, SARIKA M NAIRAbstract : For each positive integer $ n $, a square congruence graph $ S(n) $ is the graph with vertex set $ H=\left\lbrace 1,2,3,\ldots,n\right\rbrace $ and two vertices $ a , b $ are adjacent if they are distinct and $ a^{2}\equiv b^{2}\pmod n$. In this paper we investigate some structural properties of square congruence graph and we obtain the relationship between clique number, chromatic number and maximum degree of square congruence graph. Also we study square congruence graph with $ p $ vertices or $ 2p $ vertices for any prime number $ p$.
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2023-04-30
Associated curves of charged particle moving with the effect of magnetic field
Muhammed Talat Sariaydin, Aziz YazlaAbstract : Magnetic curves are the trajectories of charged particals \linebreak which are influenced by magnetic fields and they satisfy the Lorentz equation. It is important to find relationships between magnetic curves and other special curves. This paper is a study of magnetic curves and this kind of relationships. We give the relationship between $\beta $-magnetic curves and Mannheim, Bertrand, involute-evolute curves and we give some geometric properties about them. Then, we study this subject for $\gamma $-magnetic curves. Finally, we give an evaluation of what we did.
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On functions starlike with respect to $n$-ply symmetric, conjugate and symmetric conjugate points
Somya Malik, Vaithiyanathan Ravichandran
Commun. Korean Math. Soc. 2022; 37(4): 1025-1039
https://doi.org/10.4134/CKMS.c210322 -
On the structure of a $k$-annihilating ideal hypergraph of commutative rings
Shaymaa S. Essa, Husam Q. Mohammad
Commun. Korean Math. Soc. 2023; 38(1): 55-67
https://doi.org/10.4134/CKMS.c210427 -
The measurability of Hewitt-Stromberg measures and dimensions
Zied Douzi, Bilel Selmi, Haythem Zyoudi
Commun. Korean Math. Soc. 2023; 38(2): 491-507
https://doi.org/10.4134/CKMS.c220154 -
An exponentially fitted method for two parameter singularly perturbed parabolic boundary value problems
Gemechis File Duressa, Tariku Birabasa Mekonnen
Commun. Korean Math. Soc. 2023; 38(1): 299-318
https://doi.org/10.4134/CKMS.c220020
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Laplace transform and Hyers-Ulam stability of differential equation for logistic growth in a population model
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 -
The flow-curvature of curves in a geometric surface
Mircea Crasmareanu
Commun. Korean Math. Soc. 2023; 38(4): 1261-1269
https://doi.org/10.4134/CKMS.c230024 -
Soliton functions and Ricci curvatures of $D$-homothetically deformed $f$-Kenmotsu almost Riemann solitons
Urmila Biswas, Avijit Sarkar
Commun. Korean Math. Soc. 2023; 38(4): 1215-1231
https://doi.org/10.4134/CKMS.c220366 -
Results of 3-derivations and commutativity for prime rings with involution involving symmetric and skew symmetric components
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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