Generalized Fermat point
Yao Xiao, Zhang Zhao, Zhang Han, Zeng Yong
TL;DR
This paper extends the classical Fermat point concept, establishing conditions for its existence and uniqueness, and explores its geometric properties, contributing to the understanding of generalized Fermat points.
Contribution
The paper introduces a generalized Fermat point, proves conditions for its existence and uniqueness, and investigates its geometric properties, advancing classical geometric theory.
Findings
Established necessary and sufficient conditions for GFP existence and uniqueness.
Proved theorems related to the geometric properties of GFP.
Extended classical Fermat point theory to a generalized context.
Abstract
In this paper, we generalized the classical Fermat point, proved the sufficient and necessary condition for uniqueness and existence for the generalized Fermat point(GFP) theorem, and discuss some interesting geometric property of the generalized Fermat point.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Fixed Point Theorems Analysis · Mathematics and Applications