Do functional languages bring anything in the resolution of everyday business problems?
Are there any successful projects that have been implemented using a function
The Xen hypervisor is at base, implemented in OCAML; and Erlang is deployed in ultra-high reliability telephony systems (the ones that have zero down-time over periods of years).
There was a talk at the Lang.NET conference about how they'd used F# to improve the performance of an insurance application, which is about as everyday as you can get. Silverlight video, WMV video. That said, most of the focus of that talk is on F#'s concurrency support, less on the idiomatically functional aspects of the language.
I would argue that the Lotus Notes formula language is an example of a widely used real world functional programming language.
Have you heard of Lisp machines before? The emacs editor also makes extensive use of Lisp.
One implementation of Perl 6, Pugs, is written in Haskell, but it has largely given way to the standard Rakudo Perl implementation.
There are quite a few listed on Functional Programming in the Real World. From the site:
The main criterion for being real-world is that the program was written primarily to perform some task, not primarily to experiment with functional programming.