Communications of the
Korean Mathematical Society
CKMS
ISSN(Print) 1225-1763
ISSN(Online) 2234-3024
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2022-07-31
A robust numerical technique for solving non-linear Volterra integro-differential equations with boundary layer
Firat Cakir, Musa Cakir, Hayriye Guckir~CakirAbstract : In this paper, we study a first-order non-linear singularly perturbed Volterra integro-differential equation (SPVIDE). We discretize the problem by a uniform difference scheme on a Bakhvalov-Shishkin mesh. The scheme is constructed by the method of integral identities with exponential basis functions and integral terms are handled with interpolating quadrature rules with remainder terms. An effective quasi-linearization technique is employed for the algorithm. We establish the error estimates and demonstrate that the scheme on Bakhvalov-Shishkin mesh is $O(N^{-1})$ uniformly convergent, where $N$ is the mesh parameter. The numerical results on a couple of examples are also provided to confirm the theoretical analysis.
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2022-07-31
Multi-derivations and some approximations
Abasalt Bodaghi, Hassan FeizabadiAbstract : In this paper, we introduce the multi-derivations on rings and present some examples of such derivations. Then, we unify the system of functional equations defining a multi-derivation to a single formula. Applying a fixed point theorem, we will establish the generalized Hyers--Ulam stability of multi-derivations in Banach module whose upper bounds are controlled by a general function. Moreover, we give some important applications of this result to obtain the known stability outcomes.
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2022-07-31
A characterization of finite factorization positive monoids
Harold PoloAbstract : We provide a characterization of the emph{positive monoids} (i.e., additive submonoids of the nonnegative real numbers) that satisfy the finite factorization property. As a result, we establish that positive monoids with well-ordered generating sets satisfy the finite factorization property, while positive monoids with co-well-ordered generating sets satisfy this property if and only if they satisfy the bounded factorization property.
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2023-04-30
$C_{12}$-space forms
Gherici Beldjilali, Nour OubbicheAbstract : The aim of this paper is two-fold. First, we study the Chinea-Gonzalez class $C_{12}$ of almost contact metric manifolds and we discuss some fundamental properties. We show there is a one-to-one correspondence between $C_{12}$ and K\"ahlerian structures. Secondly, we give some basic results for Riemannian curvature tensor of $C_{12}$-manifolds and then establish equivalent relations among $\varphi$-sectional curvature. Concrete examples are given.
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2023-04-30
Generalized Varignon's and medial triangle theorems
Francesco LaudanoAbstract : In this paper, we extend the medial triangle theorem and Varignon's theorem to generic two-dimensional polygons and highlight the role played by diagonals in this process. One of the results is a synthetic definition of the concept of median for an $n$-sided polygon.
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2022-07-31
A translation of an analogue of Wiener space with its applications on their product spaces
Dong Hyun ChoAbstract : Let $C[0,T]$ denote an analogue of Weiner space, the space of real-valued continuous on $[0,T]$. In this paper, we investigate the translation of time interval $[0,T]$ defining the analogue of Winer space $C[0,T]$. As applications of the result, we derive various relationships between the analogue of Wiener space and its product spaces. Finally, we express the analogue of Wiener measures on $C[0,T]$ as the analogue of Wiener measures on $C[0,s]$ and $C[s,T]$ with $0
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2024-04-30
Geometric properties of starlikeness involving hyperbolic cosine function
Om P. Ahuja, Asena Çetinkaya, Sushil KumarAbstract : In this paper, we investigate some geometric properties of starlikeness connected with the hyperbolic cosine functions defined in the open unit disk. In particular, for the class of such starlike hyperbolic cosine functions, we determine the lower bounds of partial sums, Briot-Bouquet differential subordination associated with Bernardi integral operator, and bounds on some third Hankel determinants containing initial coefficients.
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2023-01-31
Some results involving the representation of the centralizer of a matrix
Smail BouargaAbstract : In this paper, we investigate the dimension and the structure of the centralizer of a square matrix with entries from an arbitrary field.
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2022-07-31
New volume comparison with almost Ricci soliton
Shahroud azami, Sakineh HajiaghasiAbstract : In this paper we consider a condition on the Ricci curvature involving vector fields which enabled us to achieve new results for volume comparison and Laplacian comparison. These results in special case obtained with considering volume non-collapsing condition. Also, by applying this condition we get new results of volume comparison for almost Ricci solitons.
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2023-01-31
Detectable means and applications
Mustapha Ra\"{\i}ssouliAbstract : In this paper, we introduce a new concept for bivariate means and we study its properties. Application of this concept for mean-inequal\-ities is also discussed. Open problems are derived as well.
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The dimension of the maximal spectrum of some ring extensions
Rachida EL KHALFAOUI, Najib Mahdou
Commun. Korean Math. Soc. 2023; 38(4): 983-992
https://doi.org/10.4134/CKMS.c220332 -
Riemannian submersions whose total space is endowed with a torse-forming vector field
\c{S}emsi Eken~Meri\c{c}, Erol K{\i}l{\i}\c{c}
Commun. Korean Math. Soc. 2022; 37(4): 1199-1207
https://doi.org/10.4134/CKMS.c210336 -
Circle approximation using parametric polynomial curves of high degree in explicit form
Young Joon Ahn
Commun. Korean Math. Soc. 2022; 37(4): 1259-1267
https://doi.org/10.4134/CKMS.c210333 -
Numerical method for a system of Caputo fractional differential equations with non-local boundary conditions
S. Joe Christin Mary, Ayyadurai Tamilselvan
Commun. Korean Math. Soc. 2023; 38(1): 281-298
https://doi.org/10.4134/CKMS.c210252
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Certain study of generalized $B$ curvature tensor within the framework of Kenmotsu manifold
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 -
Estimates for certain shifted convolution sums involving Hecke eigenvalues
Guodong Hua
Commun. Korean Math. Soc. 2023; 38(2): 319-330
https://doi.org/10.4134/CKMS.c210366 -
Knotoids, pseudo knotoids, Braidoids and pseudo braidoids on the torus
Ioannis Diamantis
Commun. Korean Math. Soc. 2022; 37(4): 1221-1248
https://doi.org/10.4134/CKMS.c210169 -
Pascal's hexagon theorem reproved by elementary tools only
Insong Choe
Commun. Korean Math. Soc. 2022; 37(4): 989-993
https://doi.org/10.4134/CKMS.c210397
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