The warped generalized Lagrange space and its application in physics

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 (e2f )i = 0.