In this paper, introducing a contraction principle on generalized metric spaces, a generalization of Banach’s fixed point theorem is obtained under the completeness condition of the space. Moreover, it is established that using such contraction principle completeness of the generalized metric space can be characterized.

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...

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}...

In this paper, we will prove several new results related to the concept of multi-valued Feng–Liu contraction. An existence, approximation and localization fixed point theorem for a generalized nonself contraction contractions in vector-valued metric spaces are proved. Stability an application system operatorial inclusions also given.

The problem ofgeneralized equilibrium problem is very general in the different subjects .Optimization problems, variational inequalities, Nash equilibrium problem and minimax problems are as special cases of generalized equilibrium problem. The purpose of this paper is to investigate the problem of approximating a common element of the set of generalized equilibrium problem, variational inequal...