Author(s)

Zengrui Kang ¹, Yuxun Zeng ²

Affiliation(s)

¹ College of Sciences, Shihezi University, Shihezi, 832000, China
² College of Water Conservancy and Civil Engineering, South China Agricultural University, Guangzhou, Guangdong, 510642, China

Corresponding Author

Zengrui Kang

ABSTRACT

Continuous function theory is a very important part of functional theory. In this paper, this article research the properties of continuous functions in the P-plane, which are commutative rings containing zero factors generated by two real number. This article overcome the difficulties arising from the zero factorisation of P-numbers and prove that continuous functions in the P-plane are bounded by the decomposition of P-numbers and a geometric interpretation is given for the boundedness of continuous functions in the P-plane. For continuous Perplex functions that satisfy zero factor decomposition, based on the decomposition of Perplex numbers, we obtain the continuous boundedness theorem for Perplex functions. This will further provide a theoretical foundation and research impetus for P-analysis and give impetus to applications of the theory of continuous functions in the p-plane in physics.

KEYWORDS

Perplex Number, Partial Order, Boundedness

CITE THIS PAPER

Zengrui Kang, Yuxun Zeng, Boundedness Theorem for Continuous Functions in the Perplex Number-plane. Transactions on Computational and Applied Mathematics (2025) Vol. 5: 21-27. DOI: http://dx.doi.org/10.23977/tracam.2025.050103.

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