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Abstract
AMS (MOS): 45B05, 45C05
The standard method for obtaining a nontrivial solution to Robin's equation is by successive approximation. The usual proof of the convergence of the sequence obtained by this iteration procedure is based on Neumann's method of arithmetic mean, and requires that the surface over which the integral operator is defined be smooth and convex. Without assuming that the surface is convex, in this paper we give a new and simpler proof of the convergence of this sequence.