Proyecciones (Antofagasta, On line)

On the incomplete fourth Appell hypergeometric matrix functions $\gamma_{4}$ and $\Gamma_{4}$

Ashish Verma — 2024-05-02

In this paper, we define the incomplete fourth Appell hypergeometric matrix functions $\gamma_{4}$ and $\Gamma_{4}$ through application of the incomplete Pochhammer matrix symbols. We also give certain properties such as matrix differential equation, integral formula, recursion formula, differentiation formula of the incomplete fourth Appell hypergeometric matrix functions $\gamma_{4}$ and $\Gamma_{4}$, where not all the matrices involved are commuting matrices.

A variant of Banach’s contraction principle in ordered Banach spaces

Abdelhamid Benmezai — 2024-05-02

In this article we establish a version of Banach’s contraction principle in ordered Banach spaces. This version is adapted to prove existence and uniqueness results for an integral equation or a boundary value problem depending on the derivative.

On Graded 1-Absorbing delta-Primary Ideals

Rashid Abu-Dawwas — 2024-05-02

Let $G$ be an abelian group with identity $0$ and let $R$ be a commutative graded ring of type $G$ with nonzero unity. Let $\mathcal{I}(R)$ be the set of all ideals of $R$ and let $\delta:\mathcal{I}(R)\longrightarrow\mathcal{I}(R)$ be a function. Then, according to (R. Abu-Dawwas, M. Refai, Graded $\delta$-Primary Structures, Bol. Soc. Paran. Mat., 40 (2022), 1-11), $\delta$ is called a graded ideal expansion of a graded ring $R$ if it assigns to every graded ideal $I$ of $R$ another graded ideal $\delta(I)$ of $R$ with $I\subseteq \delta(I)$, and if whenever $I$ and $J$ are graded ideals of $R$ with $J\subseteq I$, we have $\delta(J)\subseteq\delta(I)$. Let $\delta$ be a graded ideal expansion of a graded ring $R$. In this paper, we introduce and investigate a new class of graded ideals that is closely related to the class of graded $\delta$-primary ideals. A proper graded ideal $I$ of $R$ is said to be a graded $1$-absorbing $\delta$-primary ideal if whenever nonunit homogeneous elements $a,b,c\in R$ with $abc\in I$, then $ab\in I$ or $c\in\delta(I)$. After giving some basic properties of this new class of graded ideals, we generalize a number of results about $1$-absorbing $\delta$-primary ideals into these new graded structure. Finally, we study the graded $1$-absorbing $\delta$-primary ideals of the localization of graded rings and of the trivial graded ring extensions.