No, there is not.
A stationary point.
Krasnoselskii fixed point theorem states that under certain sircumstances the operator has at least one fixed point in a subset of a Banach space. It doesn't say anything about uniqueness of solutions, just existence, but sometimes this is usefull enough, and perhaps you can get uniqueness by some other way. I hope this answers your question
You are describing a sphere in three-dimensional space or a circle in two-dimensional space. In both cases, all points are equidistant from a single fixed point, known as the center. The fixed distance from the center to any point on the shape is called the radius.
Every point on the surface of a sphere is the same distance from a fixed point in 3-dimensional space.
A sphere
It is because many things are measured with reference to a fixed point: it space or time. This point is called a reference point or origin.
A sphere.
Sphere
A fixed location in space is a point in the three-dimensional coordinate system that remains constant and does not change its position relative to other points. It serves as a reference or anchor point for measuring distances and positions within a specific frame of reference.
A fixed location in a space is called a fixed star.
"Fixed in space" means that an object's position or orientation remains constant relative to a reference point or frame of reference. This term is often used in physics and engineering to describe an object's stability or lack of movement in a specific spatial context.
In the context of transformations, a point that does not move is often referred to as a fixed point. This means that when a transformation, such as rotation, reflection, or translation, is applied, the fixed point remains unchanged in its position. Fixed points are important in understanding the behavior of various transformations and can serve as reference points for analyzing the effects of the transformation on other points in the space.