When the observer starts moving towards the light source, the wavecrests start hitting him more frequently, which means that their speed relative to him has increased, in violation of Einstein's relativity:

http://physics.bu.edu/~redner/211-sp...9_doppler.html
"Let's say you, the observer, now move toward the source with velocity vO. You encounter more waves per unit time than you did before. Relative to you, the waves travel at a higher speed: v'=v+vO. The frequency of the waves you detect is higher, and is given by: f'=v'/λ=(v+vO)/λ."

http://a-levelphysicstutor.com/wav-doppler.php
"vO is the velocity of an observer moving towards the source. This velocity is independent of the motion of the source. Hence, the velocity of waves relative to the observer is c + vO. (...) The motion of an observer does not alter the wavelength. The increase in frequency is a result of the observer encountering more wavelengths in a given time."

https://www.youtube.com/watch?v=bg7O4rtlwEE
"Doppler effect - when an observer moves toward a stationary source. When an observer moves toward a stationary source, the period of the wave emitted by a source is shorter and the observed frequency is higher. Because the velocity of the wave relative to the observer is faster than that when it is still."

Pentcho Valev