Is the concept of relativistic mass correct?

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Foe many years We studied that mass vary as the particle velocity approaches the velocity of light. However, recently I read that that concept of variation of mass is not correct. Mass is absolute. What changes is the momentum. Hence writing that well known equation for variation of mass is not proper. We have to change our perspective, said by one of my friend. Please give your comments.
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The use of relativistic mass is "outdated". Nowadays, it is more common to work with the invariant mass, or rest mass. The result is that istead of writing [tex]p=m_r v[/tex], we write [tex]p=\gamma mv[/tex], and [tex]E=m_r c^2[/tex] becomes [tex]E=\gamma mc^2[/tex]. In the equations with the [tex]\gamma[/tex], with [tex]m_r=\gamma m[/tex] and [tex]\gamma=\left(1+\left(\frac{v}{c}\right)^2\right)^{-\frac{1}{2}}[/tex]. Nothing changes physically, tough.
 
The "relativistic mass" m=m(v) allows one to write p=mv. This seems to be nice as is looks like the well-known formula from Newtonian mechanics. But it works only for p, not for E (and other kinematical quantities). There is no way to translate E=mv²/2 via a re-definition of m=m(v). That's the reason why the relativistic mass is not very useful.

Einstein wrote in a letter (1948)
"It is not good to introduce the concept of the mass M = m/(1-v²/c²)1/2 of a body for which no clear definition can be given. It is better to introduce no other mass than 'the rest mass' m. Instead of introducing M, it is better to mention the expression for the momentum and energy of a body in motion."