quantum mechanics - Doppler effect of matter waves

1. We all know that the relativistic mass of a moving object in Special relativity increases for an observer who is measuring it for a moving object.


2. We also know the the concept of particle-wave duality.



3. We also know that the observed frequency of a wave changes according to where it is moving (away or near, transverse etc...)

Is this concept of relativistic mass increase, related to the concept of Doppler effect of matter waves?

Can other implications of Doppler effect for waves be seen for matter waves and were there any experiments done for them?

Historically, was this one of the reason for developing the concept of matter waves? (We know other reasons that are Compton effect, Interference etc....)