In this paper, we define the warped Generalized Lagrangian (WGL) spaces and then examine some of their properties. In the following, we generalize the “, Tavakol-van den Bergh”,condition in the theory of relativity(see [5]) in this space, which is an example of the application of the warped Generalized Lagrangian spaces in relativity (Theorem 4. 6). We show that condition EPS in these spaces holds provided that the warped function f satisfies the condition ( e 2f )i = 0.

Using  xed point method, we prove some new stability results for Lie ( ;  ; )-derivations and Lie C-algebra homomorphisms on Lie C-algebras associated with the Euler-Lagrange type additive functional equation....

This paper studies the concept of fuzzy Generalized topologies, which are generalizations of smooth topologies and Chang's fuzzy topologies. A basis of fuzzy Generalized topological space will be defined as functions from the family of all fuzzy subsets of a non-empty set $ X $ to $ [0, 1] $ and  some basic properties of their structure will be obtained. Some characterizations of  the basis of fuzzy Generalized topology, fuzzy Generalized cotopology and the product of fuzzy Generalized topological spaces will also be shown.

The Generalized birecurrent Finsler space have been introduced by the Finslerian geometers. The purpose of the present paper is to study three special forms of P i jkh in Generalized BP−birecurrent space. We use the properties of P2−like space, P ∗−space and P−reducible space in the main space to get new spaces that will be called a P2−like Generalized BP−birecurrent space, P ∗−Generalized BP−birecurrent space and P−reducible Generalized BP−birecurrent space, respectively. In addition, we prove that the Cartan’s first curvature tensor S i jkh satisfies the birecurrence property. Certain identities belong to these spaces have been obtained. Further, we end up this paper with some demonstrative examples.

In this paper we demonstrate the existence of a set of polynomials Pi, 1£ i £ n , which are positive semi-definite on an interval [a, b] and satisfy, partially, the conditions of polynomials found in the Lagrange interpolation process. In other words, if a=a1<…<an=b is a given finite sequence of real numbers, then Pi (aj)=dij (dij is the Kronecker delta symbol); moreover, the sum of Pi 's is identically 1.

The class of homogeneous Siklos space-times is considered from algebraic point of view and the Generalized Ricci solitons are completely classified.