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I counldn't find precise info on who/ when successfully observed relativistic mass increase. The only thing I found by a Google search is that it was first confirmed in 1908 in experiments with electrons in cathode tube.

But I know that in 1905 Einstein already produced is formula E=mc^2, and wiki says that

"Mass–energy equivalence arose originally from special relativity as a paradox described by Henri Poincaré."

Can you give a detailed chronology of the development of the notion of relativistic mass and its relation to mass-energy equivalence?

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    $\begingroup$ Did you searched for History of special relativity ? $\endgroup$
    – Mauro ALLEGRANZA
    Commented Jul 9, 2018 at 6:59
  • $\begingroup$ @MauroALLEGRANZA, thanks for the precious link, can we therefore put the the discovery at 1881 or, as the link says at 1900 with Kaufman experiment? Can you add some details or links about the experiments from Thompson to Searle? $\endgroup$
    – user157860
    Commented Jul 9, 2018 at 7:08
  • $\begingroup$ To put it shortly, the theoretical discovery of the notion of relativistic mass was made by Einstein in 1905. There were conceptual troubles with this notion at a theoretical level despite the observation of so-called mass increase in experimental results. After many years, eventually it became clear that there is no consistent formulation of the notion of relativistic mass. Today, it is clear to all physicists that there is only one mass which is related to the rest energy of particle via $E_0=mc^2$. The mis-concept of relativistic mass is put to grave today. $\endgroup$
    – ACat
    Commented Jul 10, 2018 at 2:31
  • $\begingroup$ Lev Okun must be credited for his vigorous crusade against the misconceptions in the people about the failed notion of relativistic mass $\endgroup$
    – ACat
    Commented Jul 10, 2018 at 2:32

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In theory, relativistic mass was preceded by the "electromagnetic mass" introduced by J.J. Thomson in 1881, and further developed by Heaviside (1888), Searle (1897), Poincaré (1900), Abraham (1902), Lorentz (1904).
https://en.wikipedia.org/wiki/Electromagnetic_mass

In practice, the first experiments precise enough to measure such effects were conducted by Kaufmann in 1901-1905, followed by experiments by Bucherer in 1908 and others, even though it took some time until their meaning was clarified.
https://en.wikipedia.org/wiki/Kaufmann%E2%80%93Bucherer%E2%80%93Neumann_experiments

After the advent of special relativity by Einstein in 1905, "electromagnetic mass" was superseded by the concept of "relativistic mass" first formulated by Lewis and Tolman in 1909. However, modern authors try to avoid the concept of relativistic mass, instead they use the concepts of "relativistic momentum" and "relativistic energy" in order to describe the experiments in particle accelerators, while "mass" is now simply denoted as "rest mass" or "invariant mass".
https://en.wikipedia.org/wiki/Mass_in_special_relativity#The_relativistic_mass_concept

Regarding the evolution of the mass energy equivalence: In terms of electromagnetism some elements of that concept were known to Poincaré (1900) and Hasenöhrl (1904), while the complete equivalence in terms of all forms of energy was first pointed out by Einstein in 1905. https://en.wikipedia.org/wiki/Electromagnetic_mass#Inertia_of_energy_and_radiation_paradoxes https://en.wikipedia.org/wiki/Electromagnetic_mass#Modern_view

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