Abstract: We will consider three completely new problems in the three abovementioned fields of analysis. Although all these problems at first sight have a static nature, our solutions will make essential use of a dynamical approach. As a corollary of one of results in question some unexpected sharpening of a well known Cauchy result in functional equations will be obtained.

Both the setting of the problems and the statements of the results obtained are absolutely understandable. The main ideas of the proofs will be demonstrated. No preliminary knowledge in dynamical processes will be assumed.