I require a Java jinitiator 1.3.1.28 for Ubuntu Linux

there is no jinitiator for linux, you should consult Oracle about this, there is nothing we can do about it.

if you take a read of http://blogs.oracle.com/schan/2008/01/25#a2385 then you may find that you don't need to use jinitator anymore anyway as Oracle have certified Java 1.6u2 for use, eliminating the need for Jinitiator.

If you are able to access the Oracle AP Server's 'formsweb.cfg'
(probably located in : /forms60/server/Formsweb.cfg)

Follow the instructions here:

http://www.oratransplant.nl/2005/06/16/how-to-configure-forms-to-use-sun-jpi

Search for string similar to this one:

jpi_mimetype=application/x-..............
Or
jinit_mimetype=application/x-jinit-applet;version=1.xxxxx.

Amend it to look like this :

jpi_mimetype=application/x-java-applet
Or
jinit_mimetype=application/x-java-applet

Then you should be able to access the Oracle Server via any browser with JDK/JRE plugin installed.