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The purpose of this paper is to study pseudo-Euclidean and symplectic Hom-alternative superalgebras and discuss some of their proprieties and provide construction procedures. We also introduce the notion of Rota-Baxter operators of pseudo-Euclidean Hom-alternative superalgebras of any weight and Hom-post-alternative superalgebras. A Hom-post-alternative superalgebra consists of three operations such that some compatibility conditions are satisfied. We show that a weighted Rota-Baxter operator induces a Hom-post-alternative superalgebra naturally. Conversely, a Hom-post-alternative superalgebra gives rise to a new Hom-alternative superalgebra. In particular, a Hom-pre-alternative superalgebra is naturally built via symplectic structures.

We extend the concept of Rota-Baxter operator from algebras and groups to the setting of Hom-groups. The concept of Rota-Baxter Hom-group is introduced, and fundamental properties are described. Constructions of Rota-Baxter operators for Hom-groups are obtained. We obtain Rota-Baxter Hom-subgroups, quotient Rota-Baxter Hom-groups, and demonstrate the first, second, and third isomorphism theorems of Rota-Baxter Hom-groups. A theorem on extension of the Rota-Baxter operator of a Hom-group G to the Rota-Baxter operator of a Hom-group algebra over a field K, and the conditions of existence of a homomorphism from the Hom-algebra KG into itself, through a Rota-Baxter operator of Hom-group, are obtained.

The aim of this paper is to give some constructions results of averaging operators on Hom-Lie algebras. The homogeneous averaging operators on q-deformed Witt and q-deformed W(2, 2) Hom-algebras are classified. As applications, the induced Hom-Leibniz algebra structures are obtained and their multiplicativity conditions are also given. 

In this paper, first we introduce the notion of crossed homomorphisms on Lie conformal algebras, then we construct a differential graded Lie algebra whose Maurer-Cartan elements are given by crossed homomorphisms on Lie conformal algebras. This permits us to define cohomology for crossed homomorphisms. As an application, we study infinitesimal deformations, formal deformations and extendibility of finite order deformations of crossed homomorphism between Lie conformal algebras in terms of the cohomology theory.

In this paper, fixed point results with respect to generalized rational contractive mappings in semi-metric spaces endowed with a directed graph are proved. Some examples are provided to illustrate the results. The obtained results extend, improve and generalize many results in the existing literature.

This work focuses on the properties and structures of Hom-Lie algebras of generalized sl(2)-type. We construct classes of linear twisting maps that turn a skew-symmetric algebra of generalized sl(2)-type into a Hom-Lie algebra, and identify subclasses that result in multiplicative Hom-Lie algebras. We explore ideals, Hom-ideals, subalgebras, and Hom-subalgebras, emphasizing derived series, central descending series, and nilpotence and solvability properties. We also investigate the invariance of these subalgebras under the linear twisting maps and determine whether these subalgebras are weak subalgebras, Hom-subalgebras, weak ideals, or Hom-ideals. In particular, we examine these subalgebras and properties for the subfamilies of non-multiplicative Hom-Lie algebras of generalized sl(2)-type, highlighting the differences between non-multiplicative and multiplicative cases.

The purpose of the present paper is to investigate cohomology of differential Lie algebra morphisms. First, we discuss representations of differential Lie algebra morphisms. Moreover, we construct cohomology of differential Lie algebra morphisms. As applications of our cohomology, we study formal deformations and abelian extensions of differential Lie algebra morphisms.

The purpose of this article is to examine zero-division relations between elements and ideals of general algebras using set-theoretical tools. By splitting an algebra into subsets according to zero-division relations, it is possible to establish certain zero-division rules on linear combinations and thus arbitrary elements of a given algebra. We investigate in detail these subsets, properties of zero-division relation, subsets of zero-divisors and annihilators in hom-algebras and in particular hom-associative algebras. For hom-associative algebras, we investigate properties of zero division relation subsets of the kernel of the twisting map, annihilators. Furthermore, we investigate kernels of right and left multiplication operators, ideals, hom-ideals, simplicity, hom-simplicity and domain properties for general hom-algebras and Hom-associative algebras and low-dimensional hom-associative algebras of non-associative type using the kernels of twisting maps, annihilators and their zero-division relation subsets. 

In this paper, we first introduce the notion of twisted O-operators on a Hom-Lie-Yamaguti algebra by a given (2, 3)-cocycle with coefficients in a representation. We show that a twisted O-operator induces a Hom-Lie-Yamaguti structure. We also introduce the notion of a weighted Reynolds operator on a Hom-Lie-Yamaguti algebra, which can serve as a special case of twisted O-operators on Hom-Lie-Yamaguti algebras. Then, we define a cohomology of twisted O-operator on Hom-Lie-Yamaguiti algebras with coefficients in a representation. Furthermore, we introduce and study the Hom-NS-Lie-Yamaguti algebras as the underlying structure of the twisted O-operator on Hom-Lie-Yamaguti algebras. Finally, we investigate the twisted O-operator on Hom-Lie-Yamaguti algebras induced by the twisted O-operator on Hom-Lie algebras.

In this paper, we study the generalized F-iterated function system in G-metric space. Several results of common attractors of generalized iterated function systems obtained by using generalized F-Hutchinson operators are also established. We prove that the triplet of F-Hutchinson operators defined for a finite number of general contractive mappings on a complete G-metric space is itself a generalized F-contraction mapping on a space of compact sets. We also present several examples in 2-D and 3-D for our results.