Korean Journal of Mathematics

Univariate polynomials of consecutive degrees that form a SAGBI basis

2025-08-19T14:13:20+09:00

In this paper, we provide necessary and sufficient conditions for polynomials of consecutive degrees that form a
SAGBI basis in the univariate polynomial ring. The special case of three polynomials with consecutive degrees is also considered.

Bi-Bazilevic functions based on Hurwitz-Lerch Zeta function associated with exponential Pareto distribution

2025-05-05T21:38:44+09:00

In this paper, we introduce and investigate new subclass of bi-univalent functions defined in the open unit disk, which are based on Hurwitz-Lerch Zeta function associated with exponential Pareto distribution , satisfying subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients $|a_2|$ and $|a_3|$ for functions in these new subclass. Several new consequences of the results are also pointed out.Additionally we discussed Fekete-Szegö inequality results

Generalized Lukasiewicz fuzzy subalgebras of BCI-algebras and BCK-algebras

2025-06-26T21:52:42+09:00

The aim of this paper is to generalize Lukasiewicz fuzzy subalgebras in BCK/BCI-algebras. First, the concept of (α,ϵ)-Lukasiewicz fuzzy subalgebras using fuzzy points is defined and examples to explain it are given, and then several properties are investigated. The relationship between Lukasiewicz fuzzy subalgebras and (α,ϵ)-Lukasiewicz fuzzy subalgebras is discussed, and the conditions under which the ϵ-Lukasiewicz fuzzy set to be an (α,ϵ)-Lukasiewicz fuzzy subalgebra are explored. The characterizations of (α,ϵ)-Lukasiewicz fuzzy subalgebras are examined. Conditions under which Lukasiewicz ∈-set, Lukasiewicz q-set and Lukasiewicz O-set can be subalgebras are handled.

Hyers-Ulam stability of fuzzy Hilbert $C^{}$-module homomorphisms and fuzzy Hilbert $C^{}$-module derivations

2025-06-19T22:45:27+09:00

In the present paper, we introduce the notion of a fuzzy Hilbert $C^*$-module and study the Hyers-Ulam stability of fuzzy Hilbert $C^{*}$-module homomorphisms and fuzzy Hilbert $C^{*}$-module derivations in fuzzy Hilbert $C^*$-modules using the fixed point method.

Iterated weighted projective space fibrations and toric orbifolds

2025-07-11T16:56:59+09:00

We generalize classical generalized Bott towers to orbifolds using weighted projectivizations of line bundles, which we call \emph{weighted projective towers}. From the perspective of toric topology, such a space can be constructed from a product of simplices with a rational characteristic function on it. However, such a construction gives an orbifold fibration in general. Our main theorem provides explicit criteria for when a toric orbifold over a product of simplices admits a structure of a weighted projective tower.

On the weak global dimension of a subclass of Pr\"ufer non-coherent rings

2025-06-29T16:11:16+09:00

It is known that if $R$ is a coherent Pr\"ufer ring, which is necessarily a Gaussian ring, then its weak global dimension w.gl.dim($R$) must be $0$, $1$, or $\infty$.
In this paper, we investigate the possible values of the weak global dimension for a broader class of Pr\"ufer rings that are not necessarily coherent. Our analysis employs four conceptually distinct proofs, each relying on different homological techniques, including localization at the nilradical, finitistic projective dimension, and flatness properties. The results extend the classical framework to a non-coherent setting by incorporating the effective $\mathcal{H}^D$ framework, which serves as a surrogate for coherence in controlling homological dimensions. This work aims to deepen the understanding of the weak global dimension in the context of non-coherent Pr\"ufer rings and provide a unified perspective on its behavior.

Some lower bound estimates for the generalized derivative of a polynomial

2025-03-24T22:55:15+09:00

If $P(z)$ is a polynomial of degree $n$ having all its zeros in $\left|z\right|\leq k, k\leq 1$, then Rather et al. ( Some inequalities for polynomials with restricted zeros, Ann. Univ. Ferrara, 67 (2021), 183-189.) proved that for all $z$ on $\left|z\right|=1$ for which $P(z)\neq 0,$

\begin{align*}

Re\left(z\frac{P^\prime(z)}{P(z)}\right) \geq \frac{n}{1+k}\left\lbrace 1 + \frac{k}{n}\left(\frac{k^{n}\left|a_n\right| - \left|a_0\right|}{k^{n}\left|a_n\right| + \left|a_0\right|}\right)\right\rbrace.

\end{align*}

In this paper, we extend this inequality to the generalised derivative by taking $s$-folded zeros at origin. As an application, we obtain some lower bound estimates for the generalized derivative and generalized polar derivative of a polynomial with restricted zeros, which include various results due to Tur\'{a}n, Malik, Dubinin, Aziz, Rather and Govil as special cases.

A Hopf bifurcation of multidimensional attraction-repulsion chemotaxis system with nonlinear sensitive functions

2025-07-05T10:29:44+09:00

This paper is concerned with a multi-dimensional attraction-repulsion chemotaxis system with nonlinear sensitive functions. A corresponding free boundary problem is derived, and proved the existence of stationary solutions and Hopf bifurcation which are essentially determined by the competition of attraction and repulsion.

Erratum to "Common fixed point theorem for three mappings in generalized modular metric spaces" Korean J. Math. Vol. 32 No. 1 (2024) pp.15--25

2025-09-29T18:35:25+09:00