2026-03-30
Issam ouba, Larbi Zraoula, Bouazza El Wahbi, Elmostafa Bendib
Our main objective in this paper is to introduce and study a new class of operators named demi-U-Dunford-Pettis. This class is positioned between the class of demi Dunford-Pettis operators and order weakly demicompact operators, and it contains the class of U-Dunford-Pettis operators. Specifically, we characterize the Banach lattices on which all operators are demi-U-Dunford-Pettis and examine its connections with other classes of operators. Additionally, we investigate results concerning the sum of two operators, the product of two operators, the power of operators, the domination property and operator n×n matrix of this class. Furthermore, we characterize Banach lattices for which each demi U-Dunford-Pettis operator is b-weakly demicompact (resp. demi Dunford-Pettis) and each order weakly demicompact operator (resp. b-weakly demicompact) is demi-U-Dunford-Pettis.
2026-03-30
noureddine mouslim
In this paper, we consider one-dimentional of degenerate and singular wave equations with the fractional feedback acting on one end only. First, we reformulate each system into an augmented model and using a general criteria of Arendt-Batty, we prove that our models are strongly stable. Next, by using a spectrum method, we establish nonuniform stabilization. Using a frequency domain approach we prove some polynomial energy decay rate depending on the order of the fractional derivative.
2026-03-23
Marwa GOUIAA
If X is a class of locally compact groups, a locally compact group G is called regionally X if each compact subset of G is contained in a closed X-subgroup of G. The class of regionally X groups is denoted by RX. In this paper, some general results about the structure of regionally [FD] groups are established, where [FD] denotes the class of locally compact groups G such that the topological commutator subgroup D(G) is compact. For example, if the quotient group GZ(G) modulo the center of G is regionally compact then G is regionally [FD]. On the other hand, we also show that G R[FD] is equivalent to the fact that any nite subset of G is contained in a [FD] subgroup. As an application we prove that the set compn (G) consisting of the n-tuples of elements of G contained in a common compact subgroup is a closed subgroup of the cartesian product Gn, for each positive integer n.
2026-03-23
Milan Bašić
We investigate extremal properties of vertex-degree-based graph invariants on trees, focusing primarily on the general reduced second Zagreb index $GRM_{-2}$ and the fifth Sombor-type index $SO_5$. We provide sharp lower and upper bounds for these indices in terms of the maximum degree and order of trees. Furthermore, we characterize the extremal structures attaining equality. These results provide complete solutions to several open problems recently posed in the literature concerning extremal behavior of $GRM_{-2}$ and $SO_5$ on trees.
2026-03-23
Hossam Khiamy, Salah El-Din Abbas, El- Sayed El-Sanowsy, ismail ibedou
This paper aims to propose and examine four new operators based on the fundamental structure “ideal” and the notion of “generalized” producing four new generalized ideal topological spaces. The introduced structures are explained in detail in terms of topological basic theories and some properties. Moreover, we obtain some results for the produced generalized ideal topological spaces. Also, we extend more concepts of the topological suitability for an ideal. Further, we provide several essential results related to these new frameworks. We also provide some examples to further illustrate our discussions and related findings.
2026-03-17
Wutiphol Sintunavarat, Shrijana Dhakal
This paper introduces a novel generalized iterative algorithm designed to solve the triple-hierarchical constrained optimization problem, which involves a variational inequality defined over the solution set of another variational inequality, constrained by the fixed-point set. Theoretical analysis reveals a strong convergence result for the proposed algorithm, within the rigorous framework of real Hilbert spaces. To illustrate the practical utility and robustness of the algorithm, we present several numerical examples, which not only substantiate the main theoretical results but also highlight the algorithm's capability in addressing complex and structured optimization problems with multiple layers of constraints.