Journal of the
Korean Mathematical Society

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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  • 2022-01-01

    Maximal invariance of topologically almost continuous iterative dynamics

    Byungik Kahng

    Abstract : It is known that the maximal invariant set of a continuous iterative dynamical system in a compact Hausdorff space is equal to the intersection of its forward image sets, which we will call the {\it first minimal image set}. In this article, we investigate the corresponding relation for a class of discontinuous self maps that are on the verge of continuity, or {\it topologically almost continuous endomorphisms}. We prove that the iterative dynamics of a topologically almost continuous endomorphisms yields a chain of minimal image sets that attains a unique transfinite {\it length}, which we call the {\it maximal invariance order}, as it stabilizes itself at the maximal invariant set. We prove the converse, too. Given ordinal number $\xi$, there exists a topologically almost continuous endomorphism $f$ on a compact Hausdorff space $X$ with the maximal invariance order $\xi$. We also discuss some further results regarding the maximal invariance order as more layers of topological restrictions are added.

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  • 2021-11-01

    The Ohm-Rush content function III: Completion, globalization, and power-content algebras

    Neil Epstein, Jay Shapiro

    Abstract : One says that a ring homomorphism $R \rightarrow S$ is \emph{Ohm-Rush} if extension commutes with arbitrary intersection of ideals, or equivalently if for any element $f\in S$, there is a unique smallest ideal of $R$ whose extension to $S$ contains $f$, called the \emph{content} of $f$. For Noetherian local rings, we analyze whether the completion map is Ohm-Rush. We show that the answer is typically `yes' in dimension one, but `no' in higher dimension, and in any case it coincides with the content map having good algebraic properties. We then analyze the question of when the Ohm-Rush property globalizes in faithfully flat modules and algebras over a 1-dimensional Noetherian domain, culminating both in a positive result and a counterexample. Finally, we introduce a notion that we show is strictly between the Ohm-Rush property and the weak content algebra property.

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  • 2022-05-01

    Erratum to ``Static and related critical spaces with harmonic curvature and three Ricci eigenvalues'' [J. Korean Math. Soc. 57 (2020), No. 6, pp. 1435--1449]

    Jongsu Kim

    Abstract : In this erratum, we offer a correction to [J. Korean Math. Soc. 57 (2020), No. 6, pp. 1435--1449]. Theorem 1 in the original paper has three assertions (i)-(iii), but we add (iv) after having clarified the argument.

  • 2022-03-01

    Radius constants for functions associated with a limacon domain

    Nak Eun Cho, Anbhu Swaminathan, Lateef Ahmad Wani

    Abstract : Let $\mathcal{A}$ be the collection of analytic functions $f$ defined in $\mathbb{D}:=\left\{\xi\in\mathbb{C}:|\xi|

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  • 2021-09-01

    Inclusion relations and radius problems for a subclass of starlike functions

    Prachi Gupta, Sumit Nagpal, Vaithiyanathan Ravichandran

    Abstract : By considering the polynomial function $\phi_{car}(z)=1+z+z^2/2,$ we define the class $\Scar$ consisting of normalized analytic functions $f$ such that $zf'/f$ is subordinate to $\phi_{car}$ in the unit disk. The inclusion relations and various radii constants associated with the class $\Scar$ and its connection with several well-known subclasses of starlike functions is established. As an application, the obtained results are applied to derive the properties of the partial sums and convolution.

  • 2022-05-01

    On the scaled inverse of $(x^i-x^j)$ modulo cyclotomic polynomial of the form $\Phi_{p^s}(x)$ or $\Phi_{p^s q^t}(x)$

    Jung Hee Cheon, Dongwoo Kim, Duhyeong Kim, Keewoo Lee

    Abstract : The scaled inverse of a nonzero element $a(x)\in \mathbb{Z}[x]/f(x)$, where $f(x)$ is an irreducible polynomial over $\mathbb{Z}$, is the element $b(x)\in \mathbb{Z}[x]/f(x)$ such that $a(x)b(x)=c \pmod{f(x)}$ for the smallest possible positive integer scale $c$. In this paper, we investigate the scaled inverse of $(x^i-x^j)$ modulo cyclotomic polynomial of the form $\Phi_{p^s}(x)$ or $\Phi_{p^s q^t}(x)$, where $p, q$ are primes with $p

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  • 2022-05-01

    Construction of a solution of split equality variational inequality problem for pseudomonotone mappings in Banach spaces

    Getahun Bekele Wega

    Abstract : The purpose of this paper is to introduce an iterative algorithm for approximating a solution of split equality variational inequality problem for pseudomonotone mappings in the setting of Banach spaces. Under certain conditions, we prove a strong convergence theorem for the iterative scheme produced by the method in real reflexive Banach spaces. The assumption that the mappings are uniformly continuous and sequentially weakly continuous on bounded subsets of Banach spaces are dispensed with. In addition, we present an application of our main results to find solutions of split equality minimum point problems for convex functions in real reflexive Banach spaces. Finally, we provide a numerical example which supports our main result. Our results improve and generalize many of the results in the literature.

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  • 2021-05-01

    General iterative algorithms for monotone inclusion, variational inequality and fixed point problems

    Jong Soo Jung

    Abstract : In this paper, we introduce two general iterative algorithms (one implicit algorithm and one explicit algorithm) for finding a common element of the solution set of the variational inequality problems for a continuous monotone mapping, the zero point set of a set-valued maximal monotone operator, and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. Then we establish strong convergence of the proposed iterative algorithms to a common point of three sets, which is a solution of a certain variational inequality. Further, we find the minimum-norm element in common set of three sets.

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  • 2021-01-01

    Monotonicity criterion and functional inequalities for some $q$-special functions

    Khaled Mehrez

    Abstract : Our aim in this paper is to derive several new monotonicity properties and functional inequalities of some functions involving the $q$-gamma, $q$-digamma and $q$-polygamma functions. More precisely, some classes of functions involving the $q$-gamma function are proved to be logarithmically completely monotonic and a class of functions involving the $q$-digamma function is showed to be completely monotonic. As applications of these, we offer upper and lower bounds for this special functions and new sharp upper and lower bounds for the $q$-analogue harmonic number harmonic are derived. Moreover, a number of two-sided exponential bounding inequalities are given for the $q$-digamma function and two-sided exponential bounding inequalities are then obtained for the $q$-tetragamma function.

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  • 2021-11-01

    A Liouville theorem of an integral equation of the Chern-Simons-Higgs type

    Qinghua Chen, Yayun Li, Mengfan Ma

    Abstract : In this paper, we are concerned with a Liouville-type result of the nonlinear integral equation of Chern-Simons-Higgs type \begin{equation*} u(x)=\overrightarrow{l}+C_{*}\int_{\mathbb{R}^n}\frac{(1-|u(y)|^2)|u(y)|^2u(y)-\frac{1}{2}(1-|u(y)|^2)^2u(y)}{|x-y|^{n-\alpha}}dy. \end{equation*} Here $u:\mathbb{R}^n\rightarrow \mathbb{R}^k$ is a bounded, uniformly continuous function with $k\geqslant1$ and $0

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July, 2022
Vol.59 No.4

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