  Ives-Stilwell experiment in 1938 was a historic experiment for confirming
Einstein's special relativity, and various modern types have been repeated by
use of laser technology. In this paper, we reveal and solve a long-lasting
unrecognized fundamental issue that the data analysis for all those experiments
was not consistent with Einstein's definition of the relativistic Doppler
effect so that the Doppler effect was not actually confirmed. Based on existing
data, we propose a justified data analysis and correctly confirm the Doppler
effect in the Ives-Stilwell-type experiment, thus resulting in a great advance
in the experimental verification of Lorentz invariance via the Doppler effect.
