We investigate Cartan foliations covered by fibrations. We obtain a sufficient condition for the full basic automorphism group of a complete Cartan foliation covered by fibration to admit a unique (finite-dimensional) Lie group structure in the category of Cartan foliations. The explicit new formula for determining its basic automorphism Lie group is given. Examples of computing the full basic automor\phism group of complete Cartan foliations are constructed.
In the context of modular metric spaces we prove a generalization of the Banach fixed point theorem for modular contractive mappings.
Different equivalent approaches to the notion of a foliation with transverse linear connection are