Search results for " metric space"
showing 10 items of 168 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.
George-Veeramani Fuzzy Metrics Revised
2018
In this note, we present an alternative approach to the concept of a fuzzy metric, calling it a revised fuzzy metric. In contrast to the traditional approach to the theory of fuzzy metric spaces which is based on the use of a t-norm, we proceed from a t-conorm in the definition of a revised fuzzy metric. Here, we restrict our study to the case of fuzzy metrics as they are defined by George-Veeramani, however, similar revision can be done also for some other approaches to the concept of a fuzzy metric.
Best proximity point theorems for proximal cyclic contractions
2017
The purpose of this article is to compute a global minimizer of the function $$x\longrightarrow d(x, Tx)$$ , where T is a proximal cyclic contraction in the framework of a best proximally complete space, thereby ensuring the existence of an optimal approximate solution, called a best proximity point, to the equation $$Tx=x$$ when T is not necessarily a self-mapping.
Sharp capacity estimates for annuli in weighted R^n and in metric spaces
2017
We obtain estimates for the nonlinear variational capacity of annuli in weighted R^n and in metric spaces. We introduce four different (pointwise) exponent sets, show that they all play fundamental roles for capacity estimates, and also demonstrate that whether an end point of an exponent set is attained or not is important. As a consequence of our estimates we obtain, for instance, criteria for points to have zero (resp. positive) capacity. Our discussion holds in rather general metric spaces, including Carnot groups and many manifolds, but it is just as relevant on weighted R^n. Indeed, to illustrate the sharpness of our estimates, we give several examples of radially weighted R^n, which …
Fixed Points for Multivalued Convex Contractions on Nadler Sense Types in a Geodesic Metric Space
2019
In 1969, based on the concept of the Hausdorff metric, Nadler Jr. introduced the notion of multivalued contractions. He demonstrated that, in a complete metric space, a multivalued contraction possesses a fixed point. Later on, Nadler&rsquo
A coincidence-point problem of Perov type on rectangular cone metric spaces
2017
We consider a coincidence-point problem in the setting of rectangular cone metric spaces. Using alpha-admissible mappings and following Perov's approach, we establish some existence and uniqueness results for two self-mappings. Under a compatibility assumption, we also solve a common fixed-point problem.
Fixed point theorems for fuzzy mappings and applications to ordinary fuzzy differential equations
2014
Abstract Ran and Reurings (Proc. Am. Math. Soc. 132(5):1435-1443, 2004) proved an analog of the Banach contraction principle in metric spaces endowed with a partial order and discussed some applications to matrix equations. The main novelty in the paper of Ran and Reurings involved combining the ideas in the contraction principle with those in the monotone iterative technique. Motivated by this, we present some common fixed point results for a pair of fuzzy mappings satisfying an almost generalized contractive condition in partially ordered complete metric spaces. Also we give some examples and an application to illustrate our results. MSC:46S40, 47H10, 34A70, 54E50.
Iterationsverfahren höherer Ordnung in Banach-Räumen
1969
The Newton process for operator equations in say a linear normed complete space converges under certain hypothesis about the Frechet-derivatives of the operator with at least the order two. There are different ways to improve this Newton process. For instance you obtain a process of order three if you add a correction element containing the second Frechet-derivative of the operator [1]. In the following note we will generalize this idea. In a recursive manner -- by adding higher derivatives -- we will construct iterative processes of any orderk (k > 1). A general theorem due toCollatz provides us error estimates for this processes. Last we will illustrate the processes by several examples.
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.