Various scenarios of r.f. plasma heating using fast magnetosonic and ion cyclotron waves (Bernstein modes) employing resonances at the fundamental cyclotron frequency and its harmonics for minority ions for achieving the two-component regime of fusion burning in a D+He3 plasma in toroidal and open traps are suggested. It is shown that using the omega =2 omega cd resonance for a deuteron minority in a He3 plasma and the omega = omega cHe resonance for a He3 minority in a D plasma for ion Bernstein waves with high specific powers allows one to realize the two-component regime with a power gain factor of Q approximately 0.2-0.3 at the bulk ion temperature T approximately 20-30 keV. In this case the necessary energy lifetime of the plasma appears to be an order of magnitude less than that required for the conventional scenario of fusion burning in a plasma with a Maxwellian distribution of ions (D+He3, T=60-70 keV).