At the end of the database update method I should update also the my arrayclass with this
myArrayclass.get(mContext).setsolved(id);
db.close();
at last it look like this:
public void updatecheck(int id) {
ContentValues newValues = new ContentValues();
int ok = 1;
String sutun = "tamam";
newValues.put(sutun, ok);
SQLiteDatabase db = mContext.openOrCreateDatabase(DB_NAME,
Context.MODE_PRIVATE, null);
db.update(tablename, newValues, "id = ?",
new String[] { String.valueOf(id) });
myArrayclass.get(mContext).setsolved(id);
db.close();
}