First of all thanks for the replies and for the help.
@Mike Gondek thank you very much for your suggestions, i tried with Feather but i didn't get the result that i wanted, so thanks to your screenshot i figured out that you made that effect with an extra Fill Gradient and Offset Path, it's the first time that i use Offset Path, and i'm really glad that you answered me, so now i discovered it; anyways this is what i get with another Fill Gradient plus the Offset Path effect:
as you can see into the red circle it remains a small part of the offset path that i don't want to show ( this happens cause i used a lighter pantone compared to the "background fill" for showing the tips of the curves ) and by the way sorry for my ignorance, but since english is not my mother language as you notice from my grammar errors, i wonder what Miter Limit stands for? i mean i tried to increasing and decreasing it without any result.
Anyhow if i reduce a little bit more the Offset that small part disappear but the curve it becomes a bit thinner, there's a way to remove that "unwanted small part" without reducing the width of the curves? Does the Offset Path depends also by the used font? cause i tried without bolding the font and i was getting a thinner Offset Path.
sorry for the many questions, i hope i didn't bother too much with all this stuff, thanks in advance.
Expand Appearence on the offset path creates a path independent of the original, bits of which you can then just delete, like your unwanted lower bit.