"Here's an interesting related article.
I think that whether or not violence in the media promotes violence in the viewers actions depends on many factors, ranging from time exposure, to level of interest, to will power. All minds being different, it would be hard to make a definitive generalization about this.
Violence is a very real part of life, one which almost everyone will have to deal with at some time or another, whether in sport, in conflict, or as a third-person witness. Violence has its place in society, even if only as a last resort, and this idea must not be ignored, but engaged. If one is removed from any sort of simulated violence, I should think that most would inevitably turn to their own imagination as a battlefield where violent acts can be played out. This, while not being bad in itself, can be problematic for those with an undeveloped (and thus often unhealthy) idea of how violence should be incorporated in their lives. I submit that the unconditioned mind is not only prone to constructing more horrific acts of violence than is common in mainstream media, but more importantly and relevantly, is prone to using this violence to achieve a more horrific end (the violence itself very well often being the end). Media that contains violence provides, as the above article mentions, a "psychological safety valve", which allows the consumer to experience, process, and hopefully correctly order to to their lives the violence which is presented. For this reason I believe that violence in the media should not only be tolerated, but encouraged. Now, of course, a number of caveats are in order, particularly for what purpose and with what mindset the violence is employed in the medium. If the media presents a positive view of malicious, amoral, or unnecessary violence, I can hardly think that the consumption of this work for its own benefits is a healthy habit; and of course, I always think that media should be consumed under parental consent in the case of children.
So in answer to the question, yes, in many minds I'm sure violence in the media encourages violent actions, but particularly in those who have the mental inclination towards unquestioned acceptance of what they consume as right, whose lives revolve around this type of media, who are consuming media that has improper violence (as defined above), or who have malicious tendencies in general. But beside these cases, I believe violent media fulfills an important need, both in entertainment and in development, and if treated and consumed properly, may allow us to have a healthier view of ourselves, others, and the realities of our lives.