Special relativity with generalized Lorentz transformations and Minkowski line element

We present a general formulation of special relativity with generalized Lorentz transformations and Minkowski line element. Besides the Minkowski and Euclidean metrics associated, respectively, with the Lorentz and Euclidean transformations, the general formulation can also be used to establish new forms of coordinate transformations that also leave their associated metrics invariant. We also formulate relativistic mechanics under the framework of the generalized special relativity.