Right now I am facing problem while I am trying to give web-part wise
edit & update permission to different users.

Let take a scenario as example:

I have two users ¡§A¡¨ & ¡§B¡¨.

ƒÞ User ¡§A¡¨ should have edit permission on ¡§Events¡¨ web part, at
the same time he should not edit the ¡§Image Library¡¨ web part.

ƒÞ User ¡§B¡¨ should not have edit permission on ¡§Events¡¨ web part,
at the same time he should have edit permission on the ¡§Image
Library¡¨ web part.