Hyperbolic numbers have a similar structure to complex number, which are a generalization of real numbers, but they are is an exchangeable ring containing a zero factor. The purpose of this article is to study monotone bounded theorems on the hyperbolic plane. This article breaks the limitations of previous discriminant conditions for the convergence of hyperbolic series, and propose a simple but effective of new method that provides a new discriminant condition of it. This paper provides some theoretical basis for the study of hyperboloid properties, which have a wide application background in mathematical analysis and physics. For example, in the field of mechanical and advanced engineering informatics, dynamic elastic analysis is performed using hyperbolic roofs.

Hengcheng Zhao, Bingyi Lyu. Monotone bounded theorem on the hyperbolic plane. Academic Journal of Mathematical Sciences (2024) Vol. 5, Issue 1: 58-63. https://doi.org/10.25236/AJMS.2024.050109.

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