Contraction map sets with an external factor and weakly fixed points

TL;DR

This paper introduces the property CD as a variant of the UC property, extends fixed point concepts to weak fixation, and presents a theorem for contraction map sets with an external factor.

Contribution

It defines the property CD, extends fixed point theory with weak fixation, and formulates a new theorem for contraction map sets with an external factor.

Findings

Property CD as a variant of UC property

Introduction of weak fixation of points

A new theorem for contraction map sets with an external factor

Abstract

In this paper I introduce the property CD which is a more convenient variant of the UC property and show one of the possible relationships between them, I also extend the concept of a fixed point, introducing the concept of a weak fixation of a point about a sequence. I introduce contraction map sets with an external factor and formulate a theorem for them, on which the main focus of this article falls.