Search results for " Fixed Point"
showing 10 items of 150 documents
Common fixed points in cone metric spaces for $MK$-pairs and $L$-pairs
2011
In this paper we introduce some contractive conditions of Meir-Keeler type for a pair of mappings, called $MK$-$pair$ and $L\textrm{-}pair$, in the framework of cone metric spaces and we prove theorems which assure existence and uniqueness of common fixed points for $MK$-$pairs$ and $L \textrm{-}pairs$. As an application we obtain a result of common fixed point of a $p$-$MK$-pair, a mapping and a multifunction, in complete cone metric spaces. These results extend and generalize well-known comparable results in the literature.
Common fixed points of g-quasicontractions and related mappings in 0-complete partial metric spaces
2012
Abstract Common fixed point results are obtained in 0-complete partial metric spaces under various contractive conditions, including g-quasicontractions and mappings with a contractive iterate. In this way, several results obtained recently are generalized. Examples are provided when these results can be applied and neither corresponding metric results nor the results with the standard completeness assumption of the underlying partial metric space can. MSC:47H10, 54H25.
An Integral Version of Ćirić’s Fixed Point Theorem
2011
We establish a new fixed point theorem for mappings satisfying a general contractive condition of integral type. The presented theorem generalizes the well known Ciric's fixed point theorem [Lj. B. Ciric, Generalized contractions and fixed point theorems, Publ. Inst. Math. 12 (26) (1971) 19-26]. Some examples and applications are given.
Fixed point theorems on ordered metric spaces and applications to nonlinear elastic beam equations
2012
In this paper, we establish certain fixed point theorems in metric spaces with a partial ordering. Presented theorems extend and generalize several existing results in the literature. As application, we use the fixed point theorems obtained in this paper to study existence and uniqueness of solutions for fourth-order two-point boundary value problems for elastic beam equations.
Normal forms of hyperbolic logarithmic transseries
2021
We find the normal forms of hyperbolic logarithmic transseries with respect to parabolic logarithmic normalizing changes of variables. We provide a necessary and sufficient condition on such transseries for the normal form to be linear. The normalizing transformations are obtained via fixed point theorems, and are given algorithmically, as limits of Picard sequences in appropriate topologies.
Attractors/Basin of Attraction
2020
It is a controversial issue to decide who first coined the term “attractor”. According to Peter Tsatsanis, the editor of the English version of Prédire n’est pas expliquer, it was René Thom who first introduced such a term. It is necessary, however, to remember that Thom thought that it was first introduced by the American mathe- matician Steven Smale, “although Smale says it was Thom that coined the neolo- gism “attractor”“(Tsatsanis 2010: 63–64 n. 20). From this point of view, Bob Williams expressed a more cautious opinion by saying that “the word “attractor” was invented by these guys, Thom and Smale” (Cucker and Wong 2000: 183). But other mathematicians are of the opinion that the term …
Stochastic sensitivity of bull and bear states
2021
We study the price dynamics generated by a stochastic version of a Day–Huang type asset market model with heterogenous, interacting market participants. To facilitate the analysis, we introduce a methodology that allows us to assess the consequences of changes in uncertainty on the dynamics of an asset price process close to stable equilibria. In particular, we focus on noise-induced transitions between bull and bear states of the market under additive as well as parametric noise. Our results are obtained by combining the stochastic sensitivity function (SSF) approach, a mixture of analytical and numerical techniques, due to Mil’shtein and Ryashko (1995) with concepts and techniques from th…
Process-independent strong running coupling
2016
We unify two widely different approaches to understanding the infrared behaviour of quantum chromodynamics (QCD), one essentially phenomenological, based on data, and the other computational, realised via quantum field equations in the continuum theory. Using the latter, we explain and calculate a process-independent running-coupling for QCD, a new type of effective charge that is an analogue of the Gell-Mann--Low effective coupling in quantum electrodynamics. The result is almost identical to the process-dependent effective charge defined via the Bjorken sum rule, which provides one of the most basic constraints on our knowledge of nucleon spin structure. This reveals the Bjorken sum to be…
Fixed points in weak non-Archimedean fuzzy metric spaces
2011
Mihet [Fuzzy $\psi$-contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets and Systems, 159 (2008) 739-744] proved a theorem which assures the existence of a fixed point for fuzzy $\psi$-contractive mappings in the framework of complete non-Archimedean fuzzy metric spaces. Motivated by this, we introduce a notion of weak non-Archimedean fuzzy metric space and prove that the weak non-Archimedean fuzzy metric induces a Hausdorff topology. We utilize this new notion to obtain some common fixed point results for a pair of generalized contractive type mappings.
Common fixed point theorems of integral type for OWC mappings under relaxed condition
2017
In this paper, we prove a common fixed point theorem for a pair of occasionally weakly compatible (owc) self mappings satisfying a mixed contractive condition of integral type without using the triangle inequality. We prove also analogous results for two pairs of owc self mappings by assuming symmetry only on the set of points of coincidence. These results unify, extend and complement many results existing in the recent literature. Finally, we give an application of our results in dynamic programming.