Fichera's existence principle

In mathematics, and particularly in functional analysis, Fichera's existence principle is an existence and uniqueness theorem for solution of functional equations, proved by Gaetano Fichera in 1954. More precisely, given a general vector space $V$ and two linear maps from it onto two Banach spaces, the principle states necessary and sufficient conditions for a linear transformation between the two dual Banach spaces to be invertible for every vector in $V$.