Abstract : In this paper we will demonstrate some results on a prime ring with involution by introducing two generalized derivations acting on symmetric and skew symmetric elements. This approach allows us to generalize some well known results. Furthermore, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not superfluous.
Abstract : In this paper, we studied several geometrical aspects of a perfect fluid spacetime admitting a Ricci $\rho$-soliton and an $\eta$-Ricci $\rho$-soliton. Beside this, we consider the velocity vector of the perfect fluid space time as a gradient vector and obtain some Poisson equations satisfied by the potential function of the gradient solitons.
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 : 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 : Let $\mathcal{R}$ be a $\sigma$-prime ring with involution $\sigma$. The main \linebreak objective of this paper is to describe the structure of the $\sigma$-prime ring $\mathcal{R}$ with involution $\sigma$ satisfying certain differential identities involving three derivations $\psi_1, \psi_2$ and $\psi_3$ such that $\psi_1[t_1,\sigma(t_1)]+[\psi_2(t_1),\psi_2(\sigma(t_1))] + [\psi_3(t_1),\sigma(t_1)]\in \mathcal{J}_Z$ for all $t_1\in \mathcal{R}$. Further, some other related results have also been discussed.
Abstract : In this paper, we present some estimates for the norm of a multilinear form $Tin {mathcal L}(^ml_{p}^n)$ for $1leq pleqinfty$ and $n, mgeq 2.$
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 : Our aim is to establish certain image formulas of the $(p,q)$--extended modified Bessel function of the second kind $M_{\nu,p,q} (z)$ by employing the Marichev-Saigo-Maeda fractional calculus (integral and differential) operators including their composition formulas and using certain integral transforms involving $(p,q)$--extended modified Bessel function of the second kind $M_{\nu,p,q} (z)$. Corresponding assertions for the Saigo's, 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 $(p,q)$--extended modified Bessel function of the second kind $M_{\nu,p,q} (z)$ and Fox-Wright function $_{r}\Psi_{s}(z)$.
Abstract : 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.
Abstract : We are interested in the problem of fitting a parabola to a set of data points in $mathbb{ R}^3 $. It can be usually solved by minimizing the geometric distances from the fitted parabola to the given data points. In this paper, a parabola fitting algorithm will be proposed in such a way that the sum of the squares of the geometric distances is minimized in~$mathbb{R}^3$. Our algorithm is mainly based on the steepest descent technique which determines an adequate number $ lambda $ such that $h ( lambda ) = Q ( u - lambda abla Qigl( u igr) ) < Q ( u)$. Some numerical examples are given to test our algorithm.
Sushil Kumar, Virendra Kumar
Commun. Korean Math. Soc. 2022; 37(4): 1041-1053
https://doi.org/10.4134/CKMS.c210332
Jiankui Li, Shan Li, Kaijia Luo
Commun. Korean Math. Soc. 2023; 38(2): 469-485
https://doi.org/10.4134/CKMS.c220123
Hemin A. Ahmad, Parween A. Hummadi
Commun. Korean Math. Soc. 2023; 38(2): 331-340
https://doi.org/10.4134/CKMS.c220097
Praveena Manjappa Mundalamane, Bagewadi Channabasappa Shanthappa, Mallannara Siddalingappa Siddesha
Commun. Korean Math. Soc. 2022; 37(3): 813-824
https://doi.org/10.4134/CKMS.c200471
Bui Thi Hong Cam, Nguyen Minh Tri, Do Ngoc Yen
Commun. Korean Math. Soc. 2023; 38(3): 649-661
https://doi.org/10.4134/CKMS.c220160
Asmaa Orabi Mohammed, Medhat Ahmed Rakha, Arjun K. Rathie
Commun. Korean Math. Soc. 2023; 38(3): 807-819
https://doi.org/10.4134/CKMS.c220217
Jhon J. Bravo, Jose L. Herrera
Commun. Korean Math. Soc. 2022; 37(4): 977-988
https://doi.org/10.4134/CKMS.c210367
El Mehdi Bouba , Yassine EL-khabchi, Mohammed Tamekkante
Commun. Korean Math. Soc. 2024; 39(1): 93-104
https://doi.org/10.4134/CKMS.c230134
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