Search results for "complete metric space"

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.

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

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.

Basic Sequences in the Dual of a Fréchet Space

2001

Some fixed point theorems for generalized contractive mappings in complete metric spaces

2015

We introduce new concepts of generalized contractive and generalized alpha-Suzuki type contractive mappings. Then, we obtain sufficient conditions for the existence of a fixed point of these classes of mappings on complete metric spaces and b-complete b-metric spaces. Our results extend the theorems of Ciric, Chatterjea, Kannan and Reich.

Set-Valued Generalizations of Baire′s Category Theorem

1995

Abstract We prove some generalizations of Baire′s category theorem for chains of iterates of multifunctions defined on Cech-complete spaces. In particular, we extend Lennard′s results stated for functions on complete metric spaces.

Vector-valued meromorphic functions

2002

A locally complete locally convex space E satisfies that every weakly meromorphic function defined on an open subset of \( \mathbb{C} \) with values in E is meromorphic if and only if E does not contain a countable product of copies of \( \mathbb{C} \). A characterization of locally complete spaces in the spirit of known characterizations of the (metric) convex compactness property is also given.

A property of connected Baire spaces

1997

Abstract We give a topological version of a classical result of F. Sunyer Balaguer's on a local characterization of real polynomials. This is done by studying a certain property on a class of connected Baire spaces, thus allowing us to obtain a local characterization of repeated integrals of analytic maps on Banach spaces.