Enfluencing is not to be understood as "hypnotizing", but rather trigger their appetite, their curiosity, their interest, their desire, their willing to know more, their fears, their anger… You must answer a need that will fit the character and the mood of your listener.
To put it differently, you must create an emotion that will trigger a decision. This is one of the fundamentals of radio advertising: no decision without emotion.
That's why you MUST define an angle, work your script, polish your text to trigger the emotion that comes - in this case - right before the purchase.
To influence your listeners means to shed the light on a topic he will feel concerned about - that's what's called "concerning news". Because he will feel concerned, so he will listen to you or at least will want to.
Don't forget: if you work in a commercial station, your salary comes with the task of gathering as many listeners as possible. You can't last long if you do the opposite.