Fixedpoint theorems play a fundamental role in denotational semantics of programming languages. In 1955, Tarski [6] and Davis [l] showed that a lattice L is complete if and only if every monotonic function f: L + L has a fixedpoint. Since then, other fixedpoint properties are considered, by imposing either the function to be o-continuous or the fixedpoint to be the least fixedpoint. The key que...

I give short and constructive proofs of Tarski’s fixedpoint theorem, and of Zhou’s extension of Tarski’s fixed-point theorem to set-valued maps.

In the present paper, we give a new approach to Caristi's fixed pointtheorem on non-Archimedean fuzzy metric spaces. For this we define anordinary metric $d$ using the non-Archimedean fuzzy metric $M$ on a nonemptyset $X$ and we establish some relationship between $(X,d)$ and $(X,M,ast )$%. Hence, we prove our result by considering the original Caristi's fixedpoint theorem.

this paper studies the existence of solutions for acoupled system of nonlinear fractional differential equations. newexistence and uniqueness results are established using banach fixedpoint theorem. other existence results are obtained using schaeferand krasnoselskii fixed point theorems. some illustrative examplesare also presented.

in the present paper, we give a new approach to caristi's fixed pointtheorem on non-archimedean fuzzy metric spaces. for this we define anordinary metric $d$ using the non-archimedean fuzzy metric $m$ on a nonemptyset $x$ and we establish some relationship between $(x,d)$ and $(x,m,ast )$%. hence, we prove our result by considering the original caristi's fixedpoint theorem.

OurmainpurposeofthispaperistointroducethemodifiedMannandIshikawaiteratesforfindingacommonattractivepoint of a finite family multivalued nonexpansive mappings in the setting uniformly convex Banach spaces. Weobtain necessary and sufficient conditions to guarantee strong convergence proposed algorithms withoutclosedness domain such mappings. Moreover, we derive some consequences from our main res...

Abstract In this paper, we study the resonance problem of a class of singular quasilinear parabolic equations with respect to its higher near-eigenvalues. Under a generalized Landesman-Lazer condition, it is proved that the resonance problem admits at least one nontrivial solution in weighted Sobolev spaces. The proof is based upon applying the Galerkin-type technique, the Brouwer’s fixedpoint ...

This paper presents a fixedpoint approach to inductive definitions. Instead of using a syntactic test such as “strictly positive,” the approach lets definitions involve any operators that have been proved monotone. It is conceptually simple, which has allowed the easy implementation of mutual recursion and iterated definitions. It also handles coinductive definitions: simply replace the least f...

Abstract: The paper deals with the approximate controllability of a semi-linear stochastic system with multiple delays in control in infinite dimensional spaces. Sufficient conditions for the approximate controllability of the semi-linear control system have been established. The results are obtained using the Banach fixedpoint theorem. An example is introduced to show the effectiveness of the ...

In this paper, we introduce amodifiedMann iterative process for approximating a common fixedpoint of a finite family of strict pseudo-contractions inHilbert spaces.We establish the strong convergence theorem of the general iteration scheme under some mild conditions. Our results extend and improve the recent ones announced by many others. © 2008 Elsevier Ltd. All rights reserved.