Nonlinear asymptotic mean value characterizations of holomorphic functions

¹ Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli Federico II, via Cintia, Monte S. Angelo, 80126 Napoli, Italy
² Dipartimento di Matematica ed Informatica “U. Dini”, Università di Firenze, viale Morgagni 67/A, 50134 Firenze, Italy

^* Corresponding author: riccardo.durastanti@unina.it

Received: 14 June 2023
Accepted: 9 April 2024

Abstract

Starting from a characterization of holomorphic functions in terms of a suitable mean value property, we build some nonlinear asymptotic characterizations for complex-valued solutions of certain nonlinear systems, which have to do with the classical Cauchy-Riemann equations. From these asymptotic characterizations, we derive suitable asymptotic mean value properties, which are used to construct appropriate vectorial dynamical programming principles. The aim is to construct approximation schemes for the so-called contact solutions, recently introduced by N. Katzourakis, of the nonlinear systems here considered.