Generalized/Power means in DSP
Certain varieties of generalized means have been applied in signal processing, such as the Lehmer mean. This paper discusses several generalized means, mainly from a theoretical point of view.

Note, however, that all applications of generalized means deal with signals that are inherently non-negative. This is also the case in signal processing, where there are many applications with non-negative signals, such as frequency domain denoising, image processing, fuzzy logic, etc. The application of generalized means in image processing is discussed in this thesis.

I think that rather than looking for new definitions of generalized means for bipolar signals, it is probably more useful to define the signals properly such that generalized means can be applied.

A completely different alternative to generalized means might be general non-linear filters, such as Volterra filters, which don't have the restriction that the input signal must be non-negative.