Does Relativistic Mass Influence Gravity and Energy in High-Velocity Objects?

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Ok, more precise: The meaning of "mass" is clear for all particle physicists.
I think the same is true for nuclear physics and atomic physics and I would expect it in astronomy, too.

Any other fields which deal with relativistic effects frequently?
Solid-state physics can have very low effective electron masses, but I think those are invariant (and different from the electron energy), too.
 
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mfb said:
Ok, more precise: The meaning of "mass" is clear for all particle physicists. [..]
That is imprecise. The different meanings of "mass" in the literature are clear for many physicists, but by far not clear to all. Some particle physicists use both meanings, just as is common for "time". It's because of unfamiliarity that erroneous statements are made of the kind that again appeared in this thread.
 
Some particle physicists use both meanings
I never met one who called E/c^2 "mass".
I think "time" was always used as proper time (time in the frame of the particle), too. Event timestamps are in the frame of the detector, of course.