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...

The classical method for constructing the least fixedpoint of a recursive definition is to generate a sequence of functions whose initial element is the totally undefined function and which converges to the desired least fixedpoint. This method, due to Kleene, cannot be generalized to allow the construction of other fixedpoints. In this paper we present an alternate definition of convergence an...

We introduce a fixedpoint algorithm for verifying safety properties of hybrid systems with differential equations that have right-hand sides that are polynomials in the state variables. In order to verify non-trivial systems without solving their differential equations and without numerical errors, we use a continuous generalization of induction, for which our algorithm computes the required di...

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.

In this paper, we give some new coupled common  fixed point theorems for probabilistic $varphi$-contractions  in Menger probabilistic metric spaces.  As applications of the main results, we obtain some coupled common fixed point theorems in usual metric spaces and fuzzy metric spaces. The main results of this paper improvethe corresponding results given by some authors. Finally, we give one exa...

We introduce Petruchio, a tool for computing Petri net translations of dynamic networks. To cater for unbounded architectures beyond the capabilities of existing implementations, the principle fixedpoint engine runs interleaved with coverability queries. We discuss algorithmic enhancements and provide experimental evidence that Petruchio copes with models of reasonable size.

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 ...

‎The purpose of this paper is to establish some coupled coincidence point theorems for mappings having a mixed $g$-monotone property in partially ordered metric spaces‎. ‎Also‎, ‎we present a result on the existence and uniqueness of coupled common fixed points‎. ‎The results presented in the paper generalize and extend several well-known results in the literature‎.

I show that the general implicit-function problem (or parametrized fixedpoint problem) in one complex variable has an explicit series solution given by a trivial generalization of the Lagrange inversion formula. I give versions of this formula for both analytic functions and formal power series.