Korean Journal of Mathematics

Novel insights on $\lambda$-statistically convergent sequences in neutrosophic $n$-normed linear spaces

2026-04-22T00:18:15+09:00

In this research paper, we introduce a thorough exploration of $\lambda$-statistical convergence and develop some of its interesting properties in neutrosophic $n$-normed linear spaces. Also, we define the notion of $\lambda $-statistical Cauchy sequence and prove that every neutrosophic $n$-normed linear space is $\lambda$-statistically complete. Furthermore, we study the concept of $[V,\lambda]$-summability associated with $\lambda$-statistical convergence with regard to neutrosophic $n$-norm. And we obtain the relation between statistical convergence and $\lambda$-statistical convergence within this specific framework.

Nonlinear $n$-tuple $\lambda$-Jordan $\ast$-derivations on von Neumann algebras

2026-02-09T14:36:04+09:00

Let $\mathfrak{A}$ be a factor von Neumann algebra and $\Omega$ preserves $n$-tuple $\lambda$-Jordan $\ast$-derivations on $\mathfrak{A}$, that is, for every $A_{1},A_{2},\ldots,A_{n} \in \mathfrak{A}$, \begin{eqnarray*} \Omega(A_{1}\triangleright A_{2}\triangleright\ldots \triangleright A_{n})&=&\Omega(A_{1})\triangleright A_{2}\triangleright\ldots \triangleright A_{n}+A_{1}\triangleright \Omega(A_{2})\triangleright\ldots \triangleright A_{n}\\
&&+\ldots+A_{1}\triangleright A_{2}\triangleright \ldots\triangleright \Omega(A_{n}) \end{eqnarray*} where $A_{i}\triangleright A_{j} = A_{i}A_{j} +\lambda A_{j}A_{i}^{\ast}$ for $\lambda \in \mathbb{R}$, $\lambda \notin \lbrace 0, \pm1 \rbrace$, then $\Omega$ is additive $\ast$-derivation.

Analytical study on the existence, uniqueness and stability of fractional integro-differential equations involving the modified Atangana-Baleanu operator

2026-06-24T12:46:04+09:00

The recently constructed Modified Atangana–Baleanu (MAB) fractional derivative, whose kernel is given by the generalised Mittag–Leffler function, is the subject of a class of integro-fractional differential equations that are thoroughly examined in this paper. Classical or even conventional fractional derivatives are unable to fully capture nonlocal dynamics and memory effects, but this derivative operator offers a potent tool for doing so. Complex physical, biological, and engineering systems exhibiting anomalous diffusion or hereditary behaviour can be best described by the MAB operator's versatility. We rigorously prove the existence and uniqueness of solutions to the suggested integro-fractional problem inside a suitable Banach space framework by utilising fixed-point techniques like Schauder's fixed-point theorem and the Banach contraction principle. A tangible example is provided to further bolster the analytical findings, proving the applicability and accuracy of the theoretical framework. Furthermore, the concepts of Hyers-Ulam stability and generalised Hyers-Ulam stability are examined in the stability analysis of the obtained solutions. The results of this work add to the body of knowledge on fractional differential equations and aid in the continuous creation of new fractional operators that better represent nonlocal occurrences. The proven results also pave the way for new research directions, such as numerical simulation, control, and optimisation of systems controlled by modified kernel-based fractional integro-differential equations.

Regularity of certain sandwich semigroups of linear transformations defined by the notion of character

2026-03-11T13:59:39+09:00

In 2024, Tang-On and Rakbud introduced the concept of the character of a partial linear transformation between vector spaces. Moreover, the authors defined a class of sandwich semigroups of partial linear transformations, utilizing the notion of the character. In this paper, our primary objective is to investigate the regularity of elements in these sandwich semigroups.

Hyers-Ulam stability of functional equations with parameters

2026-04-28T22:47:46+09:00

This paper explores the Hyers-Ulam stability of parameterized generalized Jensen additive and quadratic functional equations in $\beta$-homogeneous $F$-spaces, showing that approximately satisfying mappings have a unique exact approximating counterpart within a specific bound. The corresponding stability theorems are established with estimates. The results extend existing stability results to the parameterized case, enrich the theory of functional equations in $\beta$-homogeneous $F$-spaces, and provide a concise proof approach for similar equations.

A double inertial extragradient method for finite families of mappings and its application to variational inequalities

2026-04-21T16:59:22+09:00

This paper investigates the problem of finding a common solution to a variational inequality problem involving a pseudo-monotone operator and a fixed point problem for a finite family of quasi-nonexpansive mappings in real Hilbert spaces. We introduce a new double inertial Mann-type extragradient algorithm that incorporates a non-monotonic self-adaptive step size, eliminating the need for prior knowledge of the operator's Lipschitz constant. A weak convergence theorem is established for the proposed iterative method under standard assumptions. Our work extends and generalizes recent results in the literature, particularly those of Singh and Chandok (2024), to the more general setting of a finite family of mappings.

Pexider function-coefficients quadratic functional equations in Banach spaces

2026-04-28T22:55:54+09:00

The Hyers-Ulam stability of a Pexider function-coefficients quadratic functional equation in Banach spaces and the Hyers-Ulam stability of a Pexider quadratic functional equation in Banach modules are investigated by using the direct method.

Some fixed point results in $C^{\ast}$-algebra valued bipolar $b-$metric spaces

2026-04-28T23:20:26+09:00

In this paper, we prove the existence and uniqueness of fixed point and common fixed point under Banach and Kannan type contractions in the setting of $C^{\ast}$-algebra valued bipolar $b$-metric spaces. Further, few examples are given to justify the findings. Our results improve and generalize some results from the literature, at the end we give several open problems.

Optimal control results for a stochastic elastic system with structural damping and hemivariational inequalities

2026-04-24T23:58:14+09:00

This paper investigates the optimal control results for a stochastic elastic system with structural damping and hemivariational inequalities. Initially, we utilize stochastic theory, fixed point theory, and some features of Clarke's subdifferential to demonstrate the existence of a mild solution for the considered problem. Further, we establish the existence of optimal control with a corresponding cost function by employing Balder's theorem for the proposed system. At last, an illustration is given to highlight the main results.

New contractions in modular metric spaces and applications

2026-04-25T23:28:58+09:00

This article discusses new contraction mappings with reference to modular metric spaces. It examines conditions for such operators to have invariant points. A nontrivial case is shown to illustrate the veracity of the established results. From applications point of consideration, it is observed that the ideas proposed herein allow for the presentation of a general criteria for solving a class of integral equations.

Nonexistence of positive vector solutions for quasilinear Schr¨odinger systems with vanishing potentials at infinity

2026-08-17T13:16:53+09:00

We study a class of quasilinear Schr\"odinger systems arising in nonlinear optics, plasma physics, and Bose--Einstein condensates, in which the quasilinear term $\Delta(u^2)u$ induces density-dependent dispersion. Combining a change-of-variables technique for scalar quasilinear equations with the spherical-average method for elliptic systems, we prove that a nonexistence result for positive vector supersolutions of the corresponding semilinear system extends, under the same decay assumptions on the potentials, to the quasilinear system.

$\mathcal{Z}$-solitons on statistical submersions

2025-08-25T10:40:31+09:00

In this research article, we study $\mathcal{Z}$-solitons on statistical submersions with parallel vertical or horizontal distribution. Finally, we study $\mathcal{Z}$-solitons on statistical submersions with conformal or gradient potential vector field.