The curvature characteristics of particular classes Finsler spaces, such as homogeneous are one the major issues in geometry. In this paper, we have obtained expression for S-curvature space with a generalized Matsumoto metric and demonstrated that isotropic has to vanish S-curvature. We also derived mean Berwald by using formula

in this paper is introduced a new type of generalization of metric spaces called sb metric space. for this new kind of spaces it has been proved a common xed point theorem for four mappings which satisfy generalized contractive condition. we also present example to con rm our theorem.