Search results for " Mapping"

Best proximity points: Convergence and existence theorems for p-cyclic mappings

2010

Abstract We introduce a new class of mappings, called p -cyclic φ -contractions, which contains the p -cyclic contraction mappings as a subclass. Then, convergence and existence results of best proximity points for p -cyclic φ -contraction mappings are obtained. Moreover, we prove results of the existence of best proximity points in a reflexive Banach space. These results are generalizations of the results of Al-Thagafi and Shahzad (2009) [8] .

Multi-valued F-contractions and the solution of certain functional and integral equations

2013

Wardowski [Fixed Point Theory Appl., 2012:94] introduced a new concept of contraction and proved a fixed point theorem which generalizes Banach contraction principle. Following this direction of research, we will present some fixed point results for closed multi-valued F-contractions or multi-valued mappings which satisfy an F-contractive condition of Hardy-Rogers-type, in the setting of complete metric spaces or complete ordered metric spaces. An example and two applications, for the solution of certain functional and integral equations, are given to illustrate the usability of the obtained results.

Linearization of holomorphic mappings on fully nuclear spaces with a basis

1994

In [13] Mazet proved the following result.If U is an open subset of a locally convex space E then there exists a complete locally convex space (U) and a holomorphic mapping δU: U→(U) such that for any complete locally convex space F and any f ɛ ℋ (U;F), the space of holomorphic mappings from U to F, there exists a unique linear mapping Tf: (U)→F such that the following diagram commutes;The space (U) is unique up to a linear topological isomorphism. Previously, similar but less general constructions, have been considered by Ryan [16] and Schottenloher [17].

Some fixed point results for multi-valued mappings in partial metric spaces

2013

Abstract In this paper, we obtain some fixed point results for multi-valued mappings in partial metric spaces. Our results unify, generalize and complement various known comparable results from the current literature. An example is also included to illustrate the main result in the paper. MSC:46S40, 47H10, 54H25.

Construction of chaotic dynamical system

2010

The first‐order difference equation xn+ 1 = f(xn ), n = 0,1,…, where f: R → R, is referred as an one‐dimensional discrete dynamical system. If function f is a chaotic mapping, then we talk about chaotic dynamical system. Models with chaotic mappings are not predictable in long‐term. In this paper we consider family of chaotic mappings in symbol space S 2. We use the idea of topological semi‐conjugacy and so we can construct a family of mappings in the unit segment such that it is chaotic. First published online: 09 Jun 2011

Periodic and Chaotic Orbits of a Neuron Model

2015

In this paper we study a class of difference equations which describes a discrete version of a single neuron model. We consider a generalization of the original McCulloch-Pitts model that has two thresholds. Periodic orbits are investigated accordingly to the different range of parameters. For some parameters sufficient conditions for periodic orbits of arbitrary periods have been obtained. We conclude that there exist values of parameters such that the function in the model has chaotic orbits. Models with chaotic orbits are not predictable in long-term.

On a fundamental variational lemma for extremal quasiconformal mappings

1986

Geometric Properties of Planar BV -Extension Domains

2009

We investigate geometric properties of those planar domains that are extension for functions with bounded variation.We start from a characterization of such domains given by Burago–Maz'ya and prove that a bounded, simply connected domain is a BV -extension domain if and only if its com- plement is quasiconvex. We further prove that the extension property is a bi-Lipschitz invariant and give applications to Sobolev extension domains.

Caristi Type Selections of Multivalued Mappings

2015

Multivalued mappings and related selection theorems are fundamental tools in many branches of mathematics and applied sciences. In this paper we continue this theory and prove the existence of Caristi type selections for generalized multivalued contractions on complete metric spaces, by using some classes of functions. Also we prove fixed point and quasi-fixed point theorems.

Set-Valued Hardy-Rogers Type Contraction in 0-Complete Partial Metric Spaces

2014

In this paper we introduce set-valued Hardy-Rogers type contraction in 0-complete partial metric spaces and prove the corresponding theorem of fixed point. Our results generalize, extend, and unify several known results, in particular the recent Nadler’s fixed point theorem in the context of complete partial metric spaces established by Aydi et al. (2012). As an application of our results, a homotopy theorem for such mappings is derived. Also, some examples are included which show that our generalization is proper.