IUPAC naming for compounds containing carboxylic acid and anhydride together?
Acids are senior to anhydrides; therefore, a compound that contains both functional groups is named as acid.

The acid is substituted using the usual principles of substitutive nomenclature. The prefix ‘oxo’, denoting $\ce{=O}$, is used to indicate a carbonyl group when the group cannot be cited as suffix. The group $\ce{R-CO-O-{}}$ is indicated by an acyloxy prefix (e.g. ‘acetyloxy’, ‘propanoyloxy’, etc.).

For example: 3-(acetyloxy)-3-oxopropanoic acid

  

(Cyclic anhydrides, however, are named as heterocyclic pseudo ketones.)