Korean Journal of Mathematics

Modular stability results of generalized quartic functional equations by using Fatou property with $\Delta_{2}$-condition

2026-03-11T13:56:27+09:00

In this research work, we introduce a new kind of finite variable quartic functional equation and examine the Hyers-Ulam stability of this quartic functional equation in modular spaces via fixed point technique with the help of Fatou property with $\Delta_{2}$-condition. A counterexample is also provided to prove the non-stability for singular case.

Continuous Comodules

2025-12-30T19:18:28+09:00

Let $R$ be a commutative ring with unity and $C$ an $R$-coalgebra. The ring $R$ is clean if every elements $r$ in $R$ is the sum of a unit and an idempotent element of $R$. An $R$-module $M$ is clean if the endomorphism ring of $M$ over $R$ is clean. Moreover, every continuous module is clean. We adapt this idea to comodules and coalgebras. A $C$-comodule $M$ is called a clean comodule if the $C$-comodule endomorphisms of $M$ are clean. We introduce continuous comodules and proved that every continuous comodules is a clean comodules.

Normality criterion leading to counterexamples for the converse of Bloch's principle

2025-12-30T23:59:32+09:00

In this paper we establish a normality criterion related to differential in- equalities for a family of meromorphic functions which leads to some counterexamples to the converse of Bloch’s Principle. Further, we prove a normality criteria concerning non homogeneous differential polynomial that gives a partial answer to a question posed by N. Bharti and R. Kumar[Normal families concerning partially shared functions and differential polynomials, Asian-European J. of Math., 17 12, (2024)].

On right $S$-$(1,\mathcal{P})$-absorbing ideals in noncommutative rings

2026-03-02T17:05:45+09:00

We introduce and investigate the class of right $S$-$(1,\mathcal{P})$-absorbing ideals in noncommutative rings, which extends the notion of strongly $S$-$1$-absorbing primary ideals from the commutative setting. An ideal $K$ of a ring $R$ disjoint from an $m$-system $S$ is called right $S$-$(1,\mathcal{P})$-absorbing if, whenever $a,b,c \in R$ are nonunits with $aRbRc \subseteq K$, then either $ab\langle s\rangle \subseteq K$ or $c\langle s\rangle \subseteq \mathcal{P}(R)$ for some $s \in S$. We establish fundamental properties of these ideals, explore their connections with right $S$-prime and $S$-$\mathcal{P}$-ideals, and present illustrative examples. Structural results concerning localization, homomorphisms, and trivial ring extensions are obtained. In particular, we show conditions under which right $S$-$(1,\mathcal{P})$-absorbing ideals coincide with $S$-primary ideals, and we characterize their behavior in local rings. These results demonstrate how right $S$-$(1,\mathcal{P})$-absorbing ideals provide a natural framework unifying several prime-like generalizations.

On surjective $\alpha$-amplified endomorphisms of projective varieties

2026-03-02T17:00:29+09:00

Let $X$ be a projective variety of dimension $d$ over a field ${\bf k}$, and let $f:X\rightarrow X$ be a surjective endomorphism of $X$. In this paper, we prove that for any positive real number $\alpha$, any surjective, but non-isomorphic, $\alpha$-amplified endomorphism $f$ of a projective variety $X$ is of positive entropy and its first dynamical degree $\lambda_1(f)$ is not equal to $\alpha$. We also prove that for any real number $\alpha$ greater than or equal to $1$ any surjective $\alpha$-amplified endomorphism $f$ of a projective variety $X$ with positive entropy such that the set of periodic points of $f$ is Zariski dense in $X$ should be always PCD. To be more precise, we show that, when the set of all periodic points of $f_K$ is Zariski dense in $X_K$ for some uncountable algebraically closed field extension $K$ of ${\bf k}$, the set is actually countable.

Skellam distribution series related to categories of bi-univalent functions

2026-02-12T23:57:19+09:00

The Skellam distribution is a probability that describes the difference between two independent random variables following a Poisson distribution. It has been widely used to model the difference in the number of events in various fields, such as sports analysis, physics, economics, and medical statistics. More recently, this distribution has received increasing attention in mathematical studies that link probability theory to complex analysis and its applications. In this research, we present a new analytic function based on the Skellam distribution. The study leads to the construction of two new spiralike categories associated with the Gregory number. We also present a new Lemma, a generalization of the lemma adopted by Zaparwa \cite{71}, which is important for studying the Fekete-Szeg\"o inequality. Using this lemma, Fekete-Szeg\"o inequalities of the new spiralike analytic categories are derived.

Structure of rings with insertion-of-nilpotent-factors-property

2026-03-17T10:29:19+09:00

In this article, we study the structure of rings satisfying a certain insertion-of-factors property. In particular, we examine how this property interacts with various classes of rings that arise in noncommutative ring theory. These results refine and extend several known properties of IFP rings and unit-IFP rings to the setting of INFP rings.

Scatteredness of hyperspaces

2025-11-15T18:55:44+09:00

In this paper, we study separation properties on the space of closed subsets of a totally disconnected compact space. Thus we show that a topological space $X$ is scattered if and only if the corresponding hyperspace $2^X$ is also scattered under the condition of local finiteness in $X$. We also provide characterizations concerning separation properties of the hyperspace via continuous real-valued functions. Furthermore, we give some examples related to our results.

Infinite families of non-fibered twisted torus knots

2026-03-17T10:15:49+09:00

We present explicit infinite families of twisted torus knots that are not fibered. Our approach relies on an explicit formula for the Alexander polynomial derived in our previous work. We show that the leading coefficients of the Alexander polynomials of twisted torus knots can take arbitrary integer values, which immediately yields infinitely many examples of non-fibered twisted torus knots.

On linear groupoids and quadratic algebras over reals

2026-01-08T15:24:50+09:00

In this paper, we characterize quadratic algebras over reals having identity, and show that there is no proper quadratic algebra with identity satisfying the inverse axiom over reals.

Cross-sharing problems of differential polynomials of meromorphic functions

2026-03-09T19:42:00+09:00

This paper deals with the determination of meromorphic functions for which the differential polynomials or difference-differential polynomials generated by meromorphic functions f and g share a small function with weighted sharing. The results extend and generalize those obtained by Guo and Liu [7]

Differential pre-Lie bialgebras and admissible $\mathcal{S}$-equations

2026-02-13T10:47:28+09:00

The aim of this paper is to introduce the notion of differential pre-Lie bialgebra $(A,\delta,\zeta,\Phi,\Psi)$ and their admissibility conditions in terms of dual representations $(l_{\circ}^*-r_{\circ}^*,-r_{\circ}^*,\beta^*,V^*)$. Next, we show that differential pre-Lie bialgebras are characterized by matched pairs and Manin triples of differential pre-Lie algebras. Furthermore,
the coboundary case leads to the introduction of the admissible $\mathcal{S}$-equation in differential pre-Lie algebras, whose symmetric solutions are used to construct differential pre-Lie bialgebras.

$\bar{T}-$curvature and $\bar{C}-$Bochner curvature on LP-Sasakian manifolds admitting a general connection

2026-02-06T09:53:29+09:00

In the present work, it is proved that LP-Sasakian manifolds which are $\bar{T}$-flat, quasi-$\bar{T}$-flat, $\xi$-$\bar{T}$-flat, $\phi$-$\bar{T}$-flat, $\bar{T}$-semi-symmetric, $\phi$-$\bar{T}$-Ricci recurrent, $\bar{C}$-Bochner flat, or satisfy $\bar{T}\cdot\bar{S}=0$, are generalized $\eta$-Einstein manifolds. The $\bar{T}$-curvature and $\bar{C}$-Bochner curvature tensors are defined with respect to a general connection $\bar{\nabla}$ which includes the quarter-symmetric metric, Schouten--van Kampen, Tanaka--Webster, and Zamkovoy connections.

Numerical solutions for systems of nonlinear fractional differential equations using the fractional natural decomposition method

2026-05-01T15:11:36+09:00

This paper presents a complete study of the Fractional Natural Decomposition Method (FNDM) for solving systems of nonlinear fractional ordinary differential equations. The FNDM combines the Natural Transform Method with the Adomian Decomposition Method to construct analytical approximate solutions. We provide a detailed exposition of the methodology, theoretical foundations including existence, uniqueness, and convergence theorems, and applications to five distinct nonlinear systems. Recursive relations, Adomian polynomials, and numerical results are presented. Graphs illustrate the behavior of approximate solutions for different fractional orders. The results demonstrate the efficiency, accuracy, and versatility of the FNDM.