  In this work, we present a modification of explicit Runge-Kutta temporal
integration schemes that guarantees the preservation of any locally-defined
quasiconvex set of bounds for the solution. These schemes operate on the basis
of a bijective mapping between an admissible set of solutions and the real
domain to strictly enforce bounds. Within this framework, we show that it is
possible to recover a wide range of methods independently of the spatial
discretization, including positivity preserving, discrete maximum principle
satisfying, entropy dissipative, and invariant domain preserving schemes.
Furthermore, these schemes are proven to recover the order of accuracy of the
underlying Runge-Kutta method upon which they are built. The additional
computational cost is the evaluation of two nonlinear mappings which generally
have closed-form solutions. We show the utility of this approach in numerical
experiments using a pseudospectral spatial discretization without any explicit
shock capturing schemes for nonlinear hyperbolic problems with discontinuities.
