Elxed Point Theorem of Composition g-Contraction Mapping and its Applications

Any composition sequential mapping, periodic composition mapping of a complete non-empty metric space M into M with geometric mean contraction ratio less than 1(simplifying as "g-contraction mapping") has a unique fixed point in M. Applications of the theorem to the proof of existence and uniqueness of the solutions of a set of non-linear differential equations and a coupled integral equations of symmetric bending of shallow shell of revolution are given.