The axiom of choice, fixed point theorems, and inductive ordered sets

Well-ordered Sets, Ordinalities and the Axiom of Choice

The discussion of cardinalities in Chapter 2 suggests that the most interesting thing about them is their order relation, namely that any set of cardinalities forms a well-ordered set. So in this section we shall embark upon a systematic study of well-ordered sets. Remarkably, we will see that the problem of classifying sets up to bijection is literally contained in the problem of classifying w...

Fixed point theorems for $alpha$-$psi$-contractive mappings in partially ordered sets and application to ordinary differential equations

‎In this paper‎, ‎we introduce $alpha$-$psi$-contractive mapping in partially ordered sets and construct fixed point theorems to solve a first-order ordinary differential equation by existence of its lower solution.

The fixed point property for ordered sets

An ordered set P has the fixed point property iff every order-preserving self-map of P has a fixed point. This paper traces the chronological development of research on this property, including most recent developments and open questions. Mathematics Subject Classification 06A06

Ordered S-Metric Spaces and Coupled Common Fixed Point Theorems of Integral Type Contraction

In the present paper, we introduces the notion of integral type contractive mapping with respect to ordered S-metric space and prove some coupled common fixed point results of integral type contractive mapping in ordered S-metric space. Moreover, we give an example to support our main result.

Inductive properties of fixed point sets of mappings on posets and on partially ordered topological spaces