Hi Saurav,
One doubt,
i have attached the script, in that there is a function called "updateChildren" used for resolved logic.
Do you want us to use the same for closed logic as well.

Script:

function updateChildren(fields) {

if (fields.length < 1)
return;

var rec = new GlideRecord("incident");
rec.addQuery("parent_incident", current.sys_id);
rec.addQuery("state", "!=", IncidentState.RESOLVED);
rec.addActiveQuery();
rec.query();

while (rec.next()) {

for (var i = 0; i < fields.length; i++) {
rec[fields[i].name] = fields[i].value;
}

rec.update();
}
}

Advance thanks for the support.