The Walt Disney Company has created what it believes is a first-of-its-kind application allowing Facebook users to buy tickets to “Toy Story 3” without leaving the social networking site and while, at the same time, prodding their friends to come along. The application, called Disney Tickets Together, could transform how Hollywood sells movie tickets by combining purchases with the powerful forces of social networking. When you buy a ticket through Disney’s application, for instance, it alerts your Facebook friends and prompts you to invite them to buy tickets of their own. Disney quietly introduced the service on May 26 with a simple post on the site’s official “Toy Story 3” page, which has over 732,000 followers. While many theaters will not make tickets available for the film, which was made by Disney’s Pixar unit, for another week — its release date is June 18 — early results indicate that people are using the application to buy tickets in groups as large as 80, according to Disney. Disney Tickets Together, which has been in development for months, works with ticket-buying sites like Fandango.com and says it covers the majority of the movie theaters in North America. Facebook receives no percentage of the ticket sales but does, in theory, get more visitors on its site. For now, only “Toy Story 3” tickets are available. But other Disney movies would follow if the application is deemed a success.