Relativity and the Higgs field We know very well that as the velocity of an object increases, its relativistic mass also increases because of an increase in its energy which is directly equivalent to mass. We also know that the higgs field is responsible for giving mass to particles and in turn the objects make up the particles. According to our current assumption, some particles face more resistance in the higgs field and therefore end up getting more mass while some feel less resistance and end up getting a lesser mass.
Now coming to the question. Can we say that when an object is accelerated to a high velocity its particles experience more resistance from the higgs field (we can think of this in terms of friction or something) and therefore the object acquires more mass?
 A: No. What happens to an object at high speed has nothing to do with the Higgs field.
There are two errors in the argument you've made to come to this conclusion:


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*Energy is not directly equivalent to mass. An object has a certain amount of energy simply by virtue of its mass; or equivalently, an object's mass is the amount of energy it would have in the absence of external forces and at rest. But it's not the case that all energy is mass. In fact, the energy that an object gains as it moves to higher speeds does not count towards its mass, by definition; it's kinetic energy.

*The Higgs field is not responsible for giving mass to particles in the sense that I think you mean it. Only the masses of fundamental particles have anything to do with the Higgs field, but composite systems can have mass for entirely different reasons.

A: The notion of relativistic mass is an archaic one that most physicists don't use anymore. A particle's mass is a Lorentz invariant, meaning a constant property of the particle, regardless of its energy. Instead, energy and momentum are seen to be non-Lorentz invariant, such that the invariant mass remains, well, invariant:
$$E^2-p^2c^2=m^2c^4.$$
Also, the way that the Higgs field gives mass to a particle is through the Yukawa coupling, which again is particular to the particle (the heavy top quark, for example, interacts strongly with the Higgs, while the light electron has a small coupling). It's true that these couplings do vary a little bit with energy (see renormalization group), but this is a small effect.
