Amir Baklouti

This paper introduces new generalized forms of contractive mappings in the framework of complete metric spaces. By extending the classical Reich and Sehgal contractions to their iterated counterparts in Singh’s sense, we establish unified fixed-point theorems that ensure both existence and uniqueness under constant and variable contractive parameters. The proposed p-Reich and p-Sehgal contractions encompass several well-known results, including those of Banach, Kannan, Chatterjea, Reich, and Sehgal, as special cases. Convergence of the associated Picard iterative process is rigorously analyzed, revealing deeper insights into the iterative stability and asymptotic behavior of nonlinear mappings in metric spaces. The practical utility of our unified fixed-point theorems is illustrated through concrete applications in fractal and fractional calculus.

This paper complements the description of finite-dimensional Jordan symplectic metric superalgebras on algebraically closed fields of characteristic

The main purpose of this paper is to study Jacobi–Jordan-admissible algebras and some particular classes like pre-Jacobi–Jordan algebras. First, we provide characterizations of Jacobi–Jordan algebras by means of oxidation process. Then, we discuss Jacobi–Jordan-admissible algebras for which we obtain a surprising characterization as 3-power anti-associative algebras. Moreover, we introduce a concept of [ ]-anti-associative algebra, generalizing anti-associative algebras and prove that they are equivalent to Jacobi–Jordan-admissible algebras. Furthermore, we study the structure of pre-Jordan–Jacobi algebras which form a particular class of Jacobi–Jordan-admissible algebras. Moreover, an inductive description by a process of oxidation is provided for an interesting particular class of pre-Jacobi–Jordan algebras, called strong pre-Jacobi–Jordan algebras.

This paper explores the concept of Generalized Roughness in LA-Semigroups and its applications in various mathematical disciplines. We highlight the fundamental properties and structures of Generalized Roughness, examining its relationships with Fuzzy Lie Algebras, Order Theory, Lattice Structures, Algebraic Structures, and Categorical Perspectives. Moreover, we investigate the potential of mathematical modeling, optimization techniques, data analysis, and machine learning in the context of Generalized Roughness. Our findings reveal important results in Generalized Roughness, such as the preservation of roughness under the fuzzy equivalence relation and the composition of roughness sets. We demonstrate the significance of Generalized Roughness in the context of order theory and lattice structures, presenting key propositions and a theorem that elucidate its properties and relationships. Furthermore, we explore the applications of Generalized Roughness in mathematical modeling and optimization, highlighting the optimization of roughness measures, parameter estimation, and decision-making processes related to LA-Semigroup operations. We showcase how mathematical techniques can enhance understanding and utilization of LA-Semigroups in practical scenarios. Lastly, we delve into the role of data analysis and machine learning in uncovering patterns, relationships, and predictive models in Generalized Roughness. By leveraging these techniques, we provide examples and insights into how data analysis and machine learning can contribute to enhancing our understanding of LA-Semigroup behavior and supporting decision-making processes.

In multiple-attribute decision-making (MADM) problems, ranking the alternatives is an important step for making the best decision. Intuitionistic fuzzy numbers (IFNs) are a powerful tool for expressing uncertainty and vagueness in MADM problems. However, existing ranking methods for IFNs do not consider the probabilistic dominance relationship between alternatives, which can lead to inconsistent and inaccurate rankings. In this paper, we propose a new ranking method for IFNs based on the probabilistic dominance relationship and fuzzy algebras. The proposed method is able to handle incomplete and uncertain information and can generate consistent and accurate rankings.

This paper discusses the relationship between Mock-Lie algebras, Lie algebras, and Jordan algebras. It highlights the importance of the Yang–Baxter equation and symplectic forms in the study of integrable systems, quantum groups, and topological quantum field theory. The paper also proposes studying the admissible associative Yang–Baxter equation in algebras and characterizing Q-Admissible Solutions of the Associative Yang–Baxter Equation in Rota–Baxter Algebras. Finally, it discusses the interplay of coalgebra, r-matrix, and pseudo-Euclidean forms in the context of Jordan algebras and its applications in quantum groups and integrable systems.