On Unique Minimal Lᵖ-Norm Harmonic or Holomorphic Function Which Takes Given Value in a Fixed Point

First, it will be shown that Banach spaces V of harmonic or holomorphic functions with Lᵖ norm satisfy minimal norm property, i.e., in any set Vz,c:=∈ V\>|\>f(z)=c\, if nonempty, there is exactly one element with minimal norm. Later, it will be proved that this element depends continuously on a deformation of a norm and on an increasing sequence of domains in a precisely defined sense.