On Subspaces of an Almost φ-Lagrange Space

The credit for introducing the geometry of Lagrange spaces and their subspaces goes to the famous Romanian geometer Miron 1 . He developed the theory of subspaces of a Lagrange space together with Bejancu 2 . Miron and Anastasiei 3 and Sakaguchi 4 studied the subspaces of generalized Lagrange spaces GL spaces in short . Antonelli and Hrimiuc 5, 6 introduced the concept of φ-Lagrangians and studied φ-Lagrange manifolds. Generalizing the notion of a φ-Lagrange manifold, the present authors recently studied the geometry of an almost φ-Lagrange space APL space briefly and obtained the fundamental entities related to such space 7 . This paper is devoted to the subspaces of an APL space. Let F M,F x, y be an n-dimensional Finsler space and φ : R → R a smooth function. If the function φ has the following properties: