Korean Journal of Mathematics https://kkms.org/index.php/kjm <p class="p1"><span class="s1"><strong>About this Journal</strong></span></p> <p class="p1"><span class="s1">The Korean Journal of Mathematics (KJM) is the official journal of The Kangwon-Kyungki Mathematical Society (KKMS). Abbreviated title is "Korean J. Math.". This journal was launched in 1993. One volume is published each year, and each volume consists of four issues (March 30th, June 30th, September 30th, December 30th).</span></p> <p class="p1"> </p> <p class="p2"><span class="s2"><a href="http://kkms.org/index.php/kjm/about/editorialTeam"><strong>Editorial Board</strong></a></span></p> <p class="p1"> </p> <p class="p1"><span class="s1"><strong>Bibliographic Information</strong></span></p> <p class="p1"><span class="s1">pISSN: 1976-8605 (Print)<br />eISSN: 2288-1433 (Online)<br />doi: 10.11568/kjm</span></p> <p class="p1"> </p> <p class="p3"><span class="s1"><strong>Indexing and Abstracting Service</strong></span></p> <p class="p1"><span class="s1">Articles published in this journal are indexed on abstracted in Korea Citation Index (KCI), Mathematical Reviews, zbMath, Emerging Sources Citation Index (ESCI), and Scopus. </span></p> Kangwon-Kyungki Mathematical Society en-US Korean Journal of Mathematics 1976-8605 On classes of indefinite $\beta$-Kenmotsu statistical manifold https://kkms.org/index.php/kjm/article/view/1800 <p>This paper introduces the notion of lightlike hypersurfaces for a novel class of manifolds known as an indefinite nearly $\beta$-Kenmotsu statistical manifold and explores the associated geometric properties. It establishes results on the screen totally geodesic and screen totally umbilical lightlike hypersurfaces. It delineates the structure of the recurrent, Lie-recurrent and nearly recurrent structure tensor fields of lightlike hypersurfaces of an indefinite nearly $\beta-$Kenmotsu statistical manifold. Additionally, the geometry of leaves of integrable distributions of lightlike hypersurfaces in an indefinite $\beta$-Kenmotsu statistical manifold tangent to the structure vector field has been researched.</p> Shagun Bhatti Jasleen Kaur Copyright (c) 2024 Korean Journal of Mathematics https://creativecommons.org/licenses/by-nc/3.0/ 2024-12-30 2024-12-30 32 4 593 614 10.11568/kjm.2024.32.4.593 Fixed point in Banach *-algebras with an application to functional integral equation of fractional order https://kkms.org/index.php/kjm/article/view/1826 <p>In this paper, we investigate the solvability of an operator equation involving four operators in the setting of Banach *-algebras using Schauder's fixed point theorem. Moreover, we have given an application of our result to the following functional integral equation of fractional order:<br />$$<br />\xi(t)=g(t,\xi(\psi_1(t)))I^{\alpha} f_1(t,I^{\beta}u(t,\xi(\psi_2(t))))+h(t,\xi(\psi_3(t)))I^{\gamma}f_2(t,I^{\delta}v(t,\xi^*(\psi_4(t)))) <br />$$<br />for proving the existence as well as the uniqueness of the solution in Banach *-algebras under some generalized conditions.</p> Goutam Das Nilakshi Goswami Copyright (c) 2024 Korean Journal of Mathematics https://creativecommons.org/licenses/by-nc/3.0/ 2024-12-30 2024-12-30 32 4 615 628 10.11568/kjm.2024.32.4.615 A note on four dimensional summability methods https://kkms.org/index.php/kjm/article/view/1833 <p> Ishiguro studied some two dimensional summability methods in \cite{ki}. In this paper, we define the four dimensional Zweier matrix and extend the results given by Ishiguro \cite{ki} to four dimensional summability methods. We prove that an Abel summable double sequence is also summable the product of Abel and Zweier methods to the same limit. Besides this, we show the four dimensional Riesz and Zweier methods don't imply each other. In addition, we emphasize the four dimensional Zweier method implies the four dimensional Borel method.</p> Medine Yeşilkayagil Savaşcı Copyright (c) 2024 Korean Journal of Mathematics https://creativecommons.org/licenses/by-nc/3.0/ 2024-12-30 2024-12-30 32 4 629 637 10.11568/kjm.2024.32.4.629 Egodic shadowable points and uniform limits https://kkms.org/index.php/kjm/article/view/1885 <p>In this paper, we study some dynamical properties of ergodic shadowable points for dynamical systems on noncompact metric spaces. We also show that if a sequence of homeomorphisms on a metric space which converges uniformly to a homeomorphism has the ergodic shadowing property, then so does the uniform limit.</p> Namjip Koo Hyunhee Lee Copyright (c) 2024 Korean Journal of Mathematics https://creativecommons.org/licenses/by-nc/3.0/ 2024-12-30 2024-12-30 32 4 639 646 10.11568/kjm.2024.32.4.639 A new study on Simpson's type inequalities via generalized convexity with application https://kkms.org/index.php/kjm/article/view/1760 <p>Convexity plays a crucial role in the development of fractional integral inequalities. A large number of fractional integral inequalities are obtained by use of convexity methods and attributes. In this paper, we use generalized the convex functions to derive new Simpson's inequalities. Additionally, several novel connected findings of Simpson's inequality for concave functions<br>are generated. Also included in the design are several new applications to specifc real number methods.</p> Maimoona Karim Aliya Fahmi Ather Qayyum Siti Suzlin Supadi Copyright (c) 2024 Korean Journal of Mathematics https://creativecommons.org/licenses/by-nc/3.0/ 2024-12-30 2024-12-30 32 4 647 659 10.11568/kjm.2024.32.4.647 Berwald and Douglas spaces of a Finsler space with an exponential form of $(\alpha,\beta)$- metric https://kkms.org/index.php/kjm/article/view/1531 <p>In the present paper, we have undertaken a study of Berwald space and Douglas space in a Finsler space with exponential form of ($\alpha$, $\beta$)-metric. We have examined the conditions under which this metric will be a Berwald and Douglas space.</p> Brijesh Kumar Tripathi Dhruvisha Patel Copyright (c) 2024 Korean Journal of Mathematics https://creativecommons.org/licenses/by-nc/3.0/ 2024-12-30 2024-12-30 32 4 661 671 10.11568/kjm.2024.32.4.661 A study of negative arithmetic matrix with Fibonacci numbers https://kkms.org/index.php/kjm/article/view/1701 <p> In this work the Pascal matrix $P$ and the negative Pascal matrix $Q$ are studied by means of certain polynomials. We investigate an LU-factorization of $Q$ by $P$, and express the powers $Q^m$ by Fibonacci numbers.</p> jiin jo Copyright (c) 2024 Korean Journal of Mathematics https://creativecommons.org/licenses/by-nc/3.0/ 2024-12-30 2024-12-30 32 4 673 682 10.11568/kjm.2024.32.4.673 Multi-fuzzy sequences in metric spaces https://kkms.org/index.php/kjm/article/view/1734 <p>This paper introduces the concept of multi-fuzzy sequences and studies convergence within a metric space. It presents key definitions and illustrative examples, particularly focusing on the convergence of multi-fuzzy sequences, multi-fuzzy bounded sequences and multi-fuzzy Cauchy sequences. Theorems are provided to establish properties related to the uniqueness of limits and the relationships between boundedness and convergence. Furthermore, the theorems and results demonstrate connections among crisp sequences, multi-fuzzy sequences and multi-fuzzy Cauchy sequences. This article lays the groundwork for understanding the behaviour and properties of multi-fuzzy sequences.</p> Haseena C Sabu Sebastian Priyanka P Copyright (c) 2024 Korean Journal of Mathematics https://creativecommons.org/licenses/by-nc/3.0/ 2024-12-30 2024-12-30 32 4 683 693 10.11568/kjm.2024.32.4.683 A remark on regular transforms of positive closed $(1, 1)$-currents https://kkms.org/index.php/kjm/article/view/1890 <p>In this note, we prove that every regular transform of a positive closed $(1, 1)$-current on a compact K\"ahler manifold admits Lipschitz quasi-potentials. As an application, we obtain some regularity properties of the Dinh-Sibony approximation of positive closed currents in the case of bidegree $(1, 1)$.</p> Taeyong Ahn Copyright (c) 2024 Korean Journal of Mathematics https://creativecommons.org/licenses/by-nc/3.0/ 2024-12-30 2024-12-30 32 4 695 702 10.11568/kjm.2024.32.4.695 On Tauberian conditions for weighted generators of triple sequences https://kkms.org/index.php/kjm/article/view/1896 <p>This paper introduces a novel perspective on how the $(\bar{N}, p, q, r)$ method relates to $P$-convergence for triple sequences. Our main objective is to establish Tauberian conditions that govern the behavior of the weighted generator sequence $\left(z_{lmn}\right)$ concerning the sequences $\left(P_{l}\right)$, $\left(Q_{m}\right)$, and $\left(R_{n}\right)$, aiming to offer a fresh interpretation. These conditions manage the $O_{L}$- and $O$-oscillatory properties and establish a link from $(\bar{N}, p, q, r)$ summability to $P$-convergence, contingent upon specific constraints on the weight sequences. Furthermore, we demonstrate that particular instances, such as the $O_{L}$-condition of Landau type and the $O$-condition of Hardy type concerning $\left(P_{l}\right)$, $\left(Q_{m}\right)$, and $\left(R_{n}\right)$, serve as Tauberian conditions for $(\bar{N}, p, q, r)$ summability under additional conditions. Thus, our findings encompass traditional Tauberian theorems, including conditions related to gradual decline and slow oscillation in specific scenarios.</p> Asif Hussain Jan Tanweer Jalal Copyright (c) 2024 Korean Journal of Mathematics https://creativecommons.org/licenses/by-nc/3.0/ 2024-12-30 2024-12-30 32 4 703 725 10.11568/kjm.2024.32.4.703 On the N-supercyclicity of isometries on Banach spaces https://kkms.org/index.php/kjm/article/view/1911 <p>In this paper, we present a simple and self-contained proof that isometries are not $N$-supercyclic and $m$-isometries are not supercyclic, providing an alternative to the proof given by the authors in [4, 5, 11].</p> Hamid Rezaei Meysam Asadipour Copyright (c) 2024 Korean Journal of Mathematics https://creativecommons.org/licenses/by-nc/3.0/ 2024-12-30 2024-12-30 32 4 727 731 10.11568/kjm.2024.32.4.727 A canonical Christoffel transformation of the strict third degree classical linear forms https://kkms.org/index.php/kjm/article/view/1807 <p>The aim of this paper is to study several characterizations of a large family of semiclassical linear forms of class one, which are of strict third degree and are not included in either the family of symmetric forms or the quasi-symmetric family. In fact, using the Stieltjes function and the moments, we describe a canonical Christoffel transformation $w$ of the strict third degree classical linear form $\mathcal{V}_{q}^{k, l}:=\mathcal{J}(k+q/3,l-q/3), k+l\geq-1, k, l \in \mathbb{Z}, q\in\{1,2\}$, meaning $w=(x-c)\mathcal{V}_{q}^{k, l}, |c|&gt;1$.</p> Mohamed Khalfallah Copyright (c) 2024 Korean Journal of Mathematics https://creativecommons.org/licenses/by-nc/3.0/ 2024-12-30 2024-12-30 32 4 733 744 10.11568/kjm.2024.32.4.733 On the internal sum of Puiseux monoids https://kkms.org/index.php/kjm/article/view/1915 <p> In this paper, we investigate the internal (finite) sum of submonoids of rank-$1$ torsion-free abelian groups. These submonoids, when not groups, are isomorphic to nontrivial submonoids of the nonnegative cone of $\mathbb{Q}$, known as Puiseux monoids, and have been actively studied during the last few years. Here we study how the atomicity and arithmetic of Puiseux monoids behave under their internal (finite) sum inside the abelian group $\mathbb{Q}$. We study the factorization properties of such internal sums, giving priority to Cohn's notion of atomicity and the classical bounded and finite factorization properties introduced and studied in 1990 by Anderson, Anderson, and Zafrullah in the setting of integral domains, and then generalized by Halter-Koch to commutative monoids. We pay special attention to how each of the considered properties behaves under the internal sum of a Puiseux monoid with a finitely generated Puiseux monoid. Throughout the paper, we also discuss examples showing that our primary results do not hold for submonoids of torsion-free abelian groups with rank larger than $1$.</p> Jonathan Du Bryan Li Shaohuan Zhang Copyright (c) 2024 Korean Journal of Mathematics https://creativecommons.org/licenses/by-nc/3.0/ 2024-12-30 2024-12-30 32 4 745 757 10.11568/kjm.2024.32.4.745 A note on best proximity points for $F$-contractive non-self mappings https://kkms.org/index.php/kjm/article/view/1931 <pre style="-qt-block-indent: 0; text-indent: 0px; margin: 0px;">In the year 2012, Wardowski [Wardowski, D., Fixed Point Theory Appl., 94 (2012), 6pp] introduced the notion of $F$-contraction mapping and presented a fixed point result on complete metric space which generalized the Banach contraction principle. Then, in the year 2014, Omidvari et al. [Omidvari, M., Vaezpour, S.M., Saadati, R., Miskolc Math Notes, 15 (2014), 615-623] considered the concept of $F$-contraction non-self mappings and presented a best proximity point theorem for this class of mappings to generalize the fixed point theorem of Wardowski. In this note, we show that the existence of best proximity point for $F$-contraction non-self mappings follow from the Wardowski's fixed point theorem. Also, in this note, we provide a new version of [15, Theorem 2] where instead of considering the continuity of $F$-proximal contraction of the first kind, we use the concept of $p$-property. We apply Wardowski's fixed point theorem to prove [15, Theorem 2]. In the last part, we also prove a best proximity point result regarding $F$-proximal contraction of the second kind where we drop some conditions.</pre> Sumit Som Copyright (c) 2024 Korean Journal of Mathematics https://creativecommons.org/licenses/by-nc/3.0/ 2024-12-30 2024-12-30 32 4 759 768 10.11568/kjm.2024.32.4.759 Existence theorems and evaluation formulas for sequential Yeh-Feynman integrals https://kkms.org/index.php/kjm/article/view/1963 <p>We establish the existence of the sequential Yeh-Feynman integral for functionals of the form $F(x)=G(x)\Psi(x(S,T))$, where $G$ belongs to a Banach algebra of sequential Yeh-Feynman integrable functionals and $\Psi$ need not be bounded or continuous. We also give formulas evaluating the integrals of these functionals. Note that these functionals are often employed in the application of the Feynman integral to quantum theory, and $\Psi$ corresponds to the initial condition associated with Schr\"odinger equation.</p> Byoung Soo Kim Young-Hee Kim Copyright (c) 2024 Korean Journal of Mathematics https://creativecommons.org/licenses/by-nc/3.0/ 2024-12-30 2024-12-30 32 4 769 782 10.11568/kjm.2024.32.4.769 Geodesics on the Kahler cone of the Heisenberg group https://kkms.org/index.php/kjm/article/view/1949 <p> In this paper, we describe the geodesics on the K\"ahler cone of the Heisenberg group. Furthermore, we also prove that this is not a complete manifold.</p> Joonhyung Kim Ioannis Platis Li-jie Sun Copyright (c) 2024 Korean Journal of Mathematics https://creativecommons.org/licenses/by-nc/3.0/ 2024-12-30 2024-12-30 32 4 783 790 10.11568/kjm.2024.32.4.783 Generalized $\eta$-duals of Banach space valued difference sequence spaces https://kkms.org/index.php/kjm/article/view/1981 <pre>In the present paper, we get an opportunity to introduce and study the notion of generalized $\eta$-dual for Banach space valued difference sequence spaces, as a generalization of the classical $\alpha$-Köthe Toeplitz dual for scalar sequences. We obtain a set of necessary and sufficient conditions for $(A_k)\in E^\eta(X, \Delta) $, where $E \in \{ \ell_\infty,\,c,\,c_0 \}$. Moreover, we explore the notion of generalized $\eta$-dual for generalized difference sequence spaces $ E(X,\Delta^r)$ and $E(X,\Delta_\nu)$, where $r\in\mathbb{N}$ and $\nu$ is a multiplier sequence.</pre> Sandeep Kumar Naveen Sharma Copyright (c) 2024 Korean Journal of Mathematics https://creativecommons.org/licenses/by-nc/3.0/ 2024-12-30 2024-12-30 32 4 791 799 10.11568/kjm.2024.32.4.791 Two types of algebraic structures based on generalized residuated lattices https://kkms.org/index.php/kjm/article/view/1853 <p>In this paper, we introduce two types of left and right algebraic structures. We investigate the relations between bi-interior(bi-closure) operators and bi-interior(bi-closure) systems. We explore how a bi-preordered space leads to the formation of right and left rough sets.</p> Jin-Won Park Young-Hee Kim Copyright (c) 2024 Korean Journal of Mathematics https://creativecommons.org/licenses/by-nc/3.0/ 2024-12-30 2024-12-30 32 4 801 811 10.11568/kjm.2024.32.4.801 The tensor product of topological modules over a ring https://kkms.org/index.php/kjm/article/view/2016 <p>Tensor products provide an essential tool in the theory of rings and modules, but its topological structure has been rarely studied. In the present article, we give a foundational description of a natural topology on the (algebraic) tensor product of topological modules over a commutative topological ring. Our approach is to give a topology directly to the algebraic tensor product instead of introducing an universal object in the category of topological modules with respect to continuous bilinear maps.</p> Sung Myung Copyright (c) 2024 Korean Journal of Mathematics https://creativecommons.org/licenses/by-nc/3.0/ 2024-12-30 2024-12-30 32 4 813 818 10.11568/kjm.2024.32.4.813