  The classical perspective of a function is a construction which transforms a
convex function into one that is jointly convex with respect to an auxiliary
scaling variable. Motivated by applications in several areas of applied
analysis, we investigate an extension of this construct in which the scaling
variable is replaced by a nonlinear term. Our construction is placed in the
general context of locally convex spaces and it generates a lower
semicontinuous convex function under broad assumptions on the underlying
functions. Various convex-analytical properties are established and closed-form
expressions are derived. Several applications are presented.
