The well known contraction mapping principle or Banach’s fixed point theorem asserts: The method for successive substitutions converges only linearly to a fixed point of an operator equation in a Banach space setting [5], [7]. In practice, if Newton’s method is used one ignores the additional information about the contraction mapping information. Werner in [9] provided a local analysis for a Ne...

We discuss the following viscosity approximations with the weak contraction A for a nonexpansive mapping sequence {Tn}, yn αnAyn 1 − αn Tnyn, xn 1 αnAxn 1 − αn Tnxn. We prove that Browder’s and Halpern’s type convergence theorems imply Moudafi’s viscosity approximations with the weak contraction, and give the estimate of convergence rate between Halpern’s type iteration and Mouda’s viscosity ap...

BACKGROUND Catheter ablation of premature ventricular complexes (PVCs) has been used as a curative therapy in many cases. Intracardiac ultrasound with a magnetic sensor probe has recently become available for catheter ablation. In this study, we assessed a new mapping method, contraction mapping, for determining the optimal ablation sites using intracardiac ultrasound and M-mode. This study sou...

In this paper, we introduce two new concepts of Feng-Liu type multivalued contraction mapping and cyclic mapping. Then, obtain some best proximity point results for such mappings on partial metric spaces by considering Feng-Liu's technique. Finally, provide examples to show the effectiveness our results.

Certain generalized Banach's contraction mapping principles on metric spaces are unified and/or extended to Hausdorff uniform spaces. Also given are some relationships between the set of all cluster points of the Picard iterates and the set of all fixed points for the mapping. These are obtained by assuming that the latter set is nonempty and by considering certain "quasi"-contractive condition...

Mapping data to parallel computers aims at minimizing the execution time of the associated application. However, it can take an unacceptable amount of time in comparison with the execution time of the application if the size of the problem is large. In this article, first we motivate the case for graph contraction as a means for reducing the problem size. We restrict our discussion to applicati...

The probabilistic metric space as one of the important generalization of metric space was introduced by K. Menger in 1942. In this paper, we briefly discuss the historical developments of contraction mappings in probabilistic metric space with some fixed point results.

Abstract We show the theory of formal ultradifferentiable normalization. The tools utilized here are KAM methods and Contraction Mapping Principle in Banach space fixed with weighted norms.

These notes contain various versions of the contraction mapping principle. Several applications to existence theorems in the theories of differential and integral equations and variational inequalities are given. Also discussed are Hilbert’s projective metric and iterated function systems

In 1969, Kannan [1] proved a new mapping which improved the Banach Contraction theorem. The purpose of this paper is to generalize the Kannan mapping and also to prove it, in space of fractals.