Schwarz's lemma on the perplex plane

Abstract

Perplex number is an extension of complex numbers, constituting a commutative ring with zero divisors. In this paper, we primarily investigate the Schwarz lemma on the perplex plane and successfully obtain an estimation of the modulus of differentiable functions in perplex plane. Furthermore, we discuss its potential applications in complex analysis and geometric function theory. This conclusion not only offers a fresh perspective for mathematical research but also holds significant reference value for advancing studies in physics, providing valuable theoretical support for subsequent scientific investigations.