Cauchy Mean Value Theorem in Hyperbolic Plane

A Hyperbolic number is a generalization of real number. It is a commutative ring with zero factor generated by two real numbers. It is of great value in practical application. Differential mean value theorems play an important role in real analysis, one of which is Cauchy mean value theorem. By studying the correlative properties of hyperbolic numbers, this paper extends the Cauchy mean value theorem in real analysis to the hyperbolic plane, obtains the hyperbolic mean value theorem, and gives a strict proof. Hyperbolic Cauchy mean value theorem lays a further theoretical foundation for the development of hyperbolic analysis, injects new impetus to hyperbolic analysis, and improves the practical application value of hyperbolic analysis.