Axiom of Infinite Choice, transversal ordered spring spaces and fixed points

Abstract

Abstract This paper continues the study of the Axiom of Infinite Choice on transversal ordered spring spaces in terms of fixed point and increasing inductive sets. These principles unify a number of diverse results (about three thousand papers) in fixed point theory, especially recently published. Applications in partially ordered spaces and fixed point theory are also considered.

Keywords

• Fixed points
• Axiom of Infinite Choice
• Transversal ordered spring spaces
• Spaces with the non-numerical transversals
• Partially ordered spaces
• Increasing mappings