In this paper, we study nonlinear analytic methods for linear contractive operators in Banach spaces. Using these results, we obtain some new strong convergence theorems for commutative families of linear contractive operators in Banach spaces. In the results, the limit points are characterized by sunny generalized nonexpansive retractions.

We examine qualitative properties of solutions of self-consistent Poisson-NernstPlanck (PNP) systems, including uniqueness. In the case of vanishing permanent charge, the predominant case studied, our results unveil a rich structure inherent in these systems, one that is determined by the boundary conditions and the signs of the oppositely charged carrier fluxes. A particularly significant spec...

In this paper, we develop existence and uniqueness criteria to certain class of three point boundary value problems associated with third order nonlinear fuzzy differential equations, with the help of Green’s functions and contraction mapping principle.

1 Local Existence of Evolution Equations 2 1.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 The contraction mapping principle . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Local Existence for Evolution Partial Differential Equations . . . . . . . . . . . . 5 1.4 Local Existence for Nonlinear Heat and Hartree Equations . . . . . . . ...

MRI examinations may be used to monitor the progress of neurological disease. Arising structural changes can then be quantified using non-rigid registration procedures. However, the interpretation of the resulting large scale vector fields is difficult without further processing. We propose using contraction mapping to detect critical points such as attractors and repellors in order to characte...

* Correspondence: ming@mail. nhcue.edu.tw Department of Applied Mathematics, National Hsinchu University of Education, Hsin-Chu, Taiwan Full list of author information is available at the end of the article Abstract In this article, we introduce the notions of (j φ)-weak contraction mappings and (ψ φ)-weak contraction mappings in complete generalized metric spaces and prove two theorems which a...

Recommended by G ´ orniewicz Lech Here we introduce a generalisation of the Banach contraction mapping principle. We show that the result extends two existing generalisations of the same principle. We support our result by an example.

It is well known that contractive representations of the disk algebra are completely contractive. Let A denote the subalgebra of the disk algebra consisting of those functions f for which f ′(0) = 0. We prove that there are contractive representations of A which are not completely contractive, and furthermore characterize those contractive representations which are completely contractive.

p ≥2 -cyclic and contractive self-mappings on a set of subsets of a metric space which are simultaneously accretive on the wholemetric space are investigated. The joint fulfilment of the p-cyclic contractiveness and accretive properties is formulated as well as potential relationships with cyclic self-mappings in order to be Kannan self-mappings. The existence and uniqueness of best proximity p...

recently, choudhury and metiya [fixed points of weak contractions in cone metric spaces, nonlinear analysis 72 (2010) 1589-1593] proved some fixed point theorems for weak contractions in cone metric spaces. weak contractions are generalizations of the banach's contraction mapping, which have been studied by several authors. in this paper, we introduce the notion of $f$-weak contractions and als...