Near-field structures induced by multiplicative automorphisms, their limits and generalized means for complex numbers

In this paper, given a fixed near-field structure, we define the near-field structure induced by an automorphism of the underlying multiplicative group of the given near-field. For the fields C and R we give a detailed characterization of these induced fields when one assumes the multiplicative automorphism to be continuous. We define the limit systems in the space of these continuous fields. One of the significant applications of these additive structures and their limits is that they define naturally generalized power means and generalized weighted power means for any family of complex-valued variables and complex weights.