Common fixed points for isotone mappings

Monotone Generalized Contractions in Ordered Metric Spaces

“…In case (i), on using Proposition 2.1, we get d(f gx n k , f z) = 0 ∀ k ∈ N 0 and hence (14) holds for all k ∈ N 0 . In case (ii), owing to the definition of Ω, we…”

“…There exists an extensive literature on this theme, but keeping in view the requirements of this presentation, we merely refer to ( [4], [6], [9], [10], [11], [13], [14], [18], [25], [26], [38], [39], [40]). In recent years, a multitude of fixed point theorems have been proved in ordered metric spaces wherein the involved contraction conditions are merely assumed to hold on elements which are comparable in the underlying partial ordering.…”

Constructive versions of Tarski’s fixed point theorems

“…The same remark was made by numerous authors who generalized Tarski's fixed point theorem to weaken the completeness hypothesis (see among others Abian and Brown [1], Hδft [9], Pasini [15], Pelczar [16], Markowsky [14], Ward [20], Wolk [22]). This was also the case for Tarski's fixed point theorem on commuting maps (see a.o., DeMarr [6], Markowsky [14], Pelczar [17], Smithson [18], Wong [23]). Along the same lines our results could be strengthened to be applicable to partially ordered sets which are not complete lattices.…”

Fixed points in partially ordered sets

“…Commuting families. In this section we obtain an analog of Theorem A for commuting families of functions, and we extend a theorem of Tarski's [6] to commuting families of multif unctions where a family of functions is commuting in case /, g e ^~ implies that f°9 = g°f* Theorem 2.1 below is a version of a theorem of DeMarr [3]. THEOREM As a corollary we obtain an extension of a theorem of Tarski [6] …”