Abstract : The object of the present paper is to introduce a type of non-flat Riemannian manifold, called a weakly cyclic generalized $B$-symmetric manifold $(WCGBS)_{n}$. We obtain a sufficient condition for a weakly cyclic generalized $B$-symmetric manifold to be a generalized quasi Einstein manifold. Next we consider conformally flat weakly cyclic generalized $B$-symmetric manifolds. Then we study Einstein $(WCGBS)_{n}$ $(n>2)$. Finally, it is shown that the semi-symmetry and Weyl semi-symmetry are equivalent in such a manifold.
Abstract : This paper attempts to investigate a new subfamily \linebreak $\mathcal{ST}_{\vartheta ,\sigma}\left( \alpha ,\beta ,\gamma ,\mu \right) $ of spirallike functions endowed with Mittag-Leffler and Wright functions. The paper further investigates sharp coefficient bounds for functions that belong to this class.
Abstract : Hankel operators and their variants have abundant applications in numerous fields. For a non-zero complex number $r$, the $r$-Hankel operators on a Hilbert space $\mathcal{H}$ define a class of one such variant. This article introduces and explores some properties of two other variants of Hankel operators namely $k^{th}$-order $(C,r)$-Hankel operators and $k^{th}$-order $(R,r)$-Hankel operators $(k \geq 2)$ which are closely related to $r$-Hankel operators in such a way that a $k^{th}$-order $(C,r)$-Hankel matrix is formed from $r^k$-Hankel matrix on deleting every consecutive $(k-1)$ columns after the first column and a $k^{th}$-order $(R, r^k)$-Hankel matrix is formed from $r$-Hankel matrix if after the first column, every consecutive $(k-1)$ columns are deleted. For $|r| \neq 1$, the characterizations for the boundedness of these operators are also completely investigated. Finally, an appropriate approach is also presented to extend these matrices to two-way infinite matrices.
Abstract : In this paper, we study almost cosymplectic manifolds with nullity distributions admitting Riemann solitons and gradient almost Riemann solitons. First, we consider Riemann soliton on $(\kappa, \mu)$-almost cosymplectic manifold $M$ with $\kappa<0$ and we show that the soliton is expanding with $\lambda = \frac{\kappa}{2n-1}(4n-1)$ and $M$ is locally isometric to the Lie group $G_\rho$. Finally, we prove the non-existence of gradient almost Riemann soliton on a $(\kappa, \mu)$-almost cosymplectic manifold of dimension greater than 3 with $\kappa < 0$.
Abstract : Given a linear connection $\nabla$ and its dual connection $\nabla^*$, we discuss the situation where $\nabla +\nabla^* = 0$. We also discuss statistical manifolds with torsion and give new examples of some type for linear connections inducing the statistical manifolds with non-zero torsion.
Abstract : In this paper, we prove the Hyers-Ulam stability and Mittag-Leffler-Hyers-Ulam stability of a differential equation of Logistic growth in a population by applying Laplace transforms method.
Abstract : In this paper, we prove $L^{p}$ estimates of a class of singular integral operators on product domains along surfaces defined by mappings that are more general than polynomials and convex functions. We assume that the kernels are in $L(\log L)^{2}(\mathbb{S}^{n-1}\times \mathbb{S}^{m-1})$. Furthermore, we\ prove $L^{p}$ estimates of the related class of Marcinkiewicz integral operators. Our results extend as well as improve previously known results.
Abstract : 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.
Abstract : 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$.
Abstract : In the present paper, following the pullback approach to Finsler geometry, we study intrinsically the $C^v$-reducible and generalized $C^v$-reducible Finsler spaces. Precisely, we introduce a coordinate-free formulation of these manifolds. Then, we prove that a Finsler manifold is $C^v$-reducible if and only if it is $C$-reducible and satisfies the $\mathbb{T}$-condition. We study the generalized $C^v$-reducible Finsler manifold with a scalar $\pi$-form $\mathbb{A}$. We show that a Finsler manifold $(M,L)$ is generalized $C^v$-reducible with $\mathbb{A}$ if and only if it is $C$-reducible and $\mathbb{T}=\mathbb{A}$. Moreover, we prove that a Landsberg generalized $C^v$-reducible Finsler manifold with a scalar $\pi$-form $\mathbb{A}$ is Berwaldian. Finally, we consider a special $C^v$-reducible Finsler manifold and conclude that a Finsler manifold is a special $C^v$-reducible if and only if it is special semi-$C$-reducible with vanishing $\mathbb{T}$-tensor.
Uday Chand De, Mohammad Nazrul Islam Khan
Commun. Korean Math. Soc. 2023; 38(4): 1233-1247
https://doi.org/10.4134/CKMS.c230006
Uday Chand De, Dipankar Hazra
Commun. Korean Math. Soc. 2024; 39(1): 201-210
https://doi.org/10.4134/CKMS.c230105
Souad DAKIR, Hajar EL MIR, Abdellah MAMOUNI
Commun. Korean Math. Soc. 2024; 39(1): 1-10
https://doi.org/10.4134/CKMS.c230052
Rahuthanahalli Thimmegowda Naveen Kumar, Basavaraju Phalaksha Murthy, Puttasiddappa Somashekhara, Venkatesha Venkatesha
Commun. Korean Math. Soc. 2023; 38(3): 893-900
https://doi.org/10.4134/CKMS.c220287
Souad DAKIR, Hajar EL MIR, Abdellah MAMOUNI
Commun. Korean Math. Soc. 2024; 39(1): 1-10
https://doi.org/10.4134/CKMS.c230052
soufiane Benkouider, Abita Rahmoune
Commun. Korean Math. Soc. 2023; 38(3): 943-966
https://doi.org/10.4134/CKMS.c220225
Uday Chand De, Aydin Gezer, Cagri Karaman
Commun. Korean Math. Soc. 2023; 38(3): 837-846
https://doi.org/10.4134/CKMS.c220031
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
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