Integral Monotonicity on the Duplex-Plane

Duplex numbers are a generalization of real numbers, which are commutable rings with zero factors generated by two real numbers. In this paper, according to the partial order relationship of the duplex number and the decomposition of the duplex number, the monotonicity of the integral on the duplex-plane is studied, and the monotonic representation of the duplex-integral is obtained. This paper finds two null factors in the definition of the expression of the duplex number, and decompose them on this basis, which is helpful for us to analyze its monotonic nature. The monotonicity of the duplex integral will further promote the development of the theory of duplex analysis.