Lagrange's mean value theorem in hyperbolic number plane

Abstract

Hyperbolic number is a generalization of real number, it is a commutative ring of zero factor, and has been widely used in many fields such as mathematics, physics and engineering. In this paper, we first review the basic concepts and properties of hyperbolic numbers, and then study the Lagrange's mean value theorem on the hyperbolic numbers plane, and get a more general theorem. This not only provides impetus for the development of hyperbolic analysis, but also further injects energy into the development of applied mathematics.