Does due process require the State to provide meaningful procedural safeguards when responding to judicial petitions?

QUESTION PRESENTED ; Ghosh owned two adjacent buildings in Berkeley, and the coplaintiff, International Institute of Bengal Basin (IIBB) occupied one of them. In a pending lawsuit, petitioners filed a third amended complaint, alleging that newly discovered evidence showed that the newly-named defendants conspired with the other defendants to deprive them of their property and arrange for it to be sold at a below-market price to some of the new defendants. _ The trial court sustained demurrers by the defendants, and Ghosh and IIBB sought to appeal. _ Because Petitioner Ghosh had been found to be a vexatious , litigant, he had to make application to the presiding justice of the Court of Appeal for permission to appeal, and show that the appeal had merit. He made application, and pointed out numerous (and sometimes obvious) errors the trial court had made in sustaining the demurrer. The appellate court denied the Application, stating only, “Mr. Ghosh has failed to show a reasonable possibility that his appeal has merit.” The question presented is, does due process affirmatively require the State to provide meaningful procedural safeguards when it responds to judicial petitions?