arXiv subjects

Trinh Tung

Publications and source records attributed to Trinh Tung.

4 recordsLinked to original sources

arXiv2026

Granular fractional Caputo-Katugampola derivatives and their applications in optimality conditions for fuzzy fractional variational problems

In this article, we present the new definition of the fuzzy Caputo-Katugampola derivative and its related concepts for the class of fuzzy functions and apply them to establish both necessary and sufficient optimality conditions for fractional fuzzy variational problems. By adopting the horizontal membership functional representation of fuzzy numbers, the granular Caputo-Katugampola derivatives offer higher computational efficiency than the previous approaches in certain scenarios. The optimality conditions for the fuzzy fractional variational problems under granular fuzzy Caputo fractional derivatives are also examined and illustrated with detailed examples. Another novel aspect of our results, even in the non-fuzzy case, is the application of special functions to represent the exact solutions of the fuzzy fractional variational problems.

math.GM↗

arXiv2026

Continuous solutions of Dirichlet problem to Hessian type equations for $(\omega,m)-\beta$-subharmonic functions on a ball in $\mathbb{C}^n$

In this paper, we investigate the continuity of solutions to the Dirichlet problem for complex Hessian-type equations associated with $(\omega, m)-\beta$-subharmonic functions on a ball in $\mathbb{C}^n$, where $ \beta=d d^c\|z\|^2=\frac{i}{2} \sum_{j=1}^n d z_j \wedge d \bar{z}_j $ is denoted the flat metric on $\mathbb{C}^n$.

math.CV↗

arXiv2026

Continuity of the complex Monge-Amp\`ere operator on compact Hermitian manifolds

In this note, we establish several results concerning the continuity (or weak convergence) of the complex Monge-Amp\`ere operator on compact Hermitian manifolds. At the end of this note, we find a weak solution of the complex Monge-Amp\`ere equation on a compact Hermitian manifold under the assumption of the existence of a smooth subsolution.

math.CV↗

arXiv2025

On Lelong numbers of plurisubharmonic functions on complex spaces

In this paper, we introduce the notion of strong locally irreducible complex spaces $\widetilde{X}$. Based on this notion we prove the equality $\barν_φ(x)=$ mult$(\widetilde{X},x). ν_φ(x)$ for all $x\in \widetilde{X}$, where $\barν_φ(x)$ is the projective mass of a plurisubharmonic function $φ$ at $x$ and mult$(\widetilde{X},x)$ is the multiplicity of $\widetilde{X}$ at $x$ and $ν_φ(x)$ is Lelong number of $φ$ at $x$. Moreover, we show that the closure of the upper-level sets $\{z\in \widetilde{X}:ν_φ(z)\geq c\}$ of a plurisubharmonic function $φ$ on a strong locally irreducible complex space $\widetilde{X}$ is a subvariety of $\widetilde{X}$ for all $c\geq 0$.

math.CV↗