Fixed Point Theory in Ordered Sets and Applications

Monotone convergence theorems for Henstock–Kurzweil integrable functions and applications

“…In [3,10] a monotone convergence theorem has been proved for order bounded sequences of HL (Henstock-Lebesgue) integrable functions which are also Bochner integrable, but not necessarily HK integrable (see [18]). Also a dominated convergence theorem has been proved in [3,10] for order bounded sequences of HL integrable functions.…”

An abstract point of view on iterative approximation schemes of fixed points for multivalued operators

“…By definition, the multivalued operator T is called increasing (see [46] and [16]; see also [5], [10]) if and only if…”

Invariant sets and Knaster-Tarski principle

“…For various applications of fixed point theorems on posets the reader can browse [18,26,29,32,36,37,49,62,63,66].…”

“…Nevertheless spaces of sets are naturally ordered by inclusion. This yields an opportunity to employ order theoretic techniques [18,38,67,72].…”