In [9], Agarwal considered a contraction restricted with a positive linear mapping and proved the following fixed point theorem in cone metric spaces.
A simple and natural way to unify and prove in a simple manner several metrical fixed point theorems is to consider an implicit contraction type condition instead of the usual explicit contractive conditions.
However, the involved mapping f is usually considered as a contraction.
Ms Yellen may be forced to consider an expansion, rather than a contraction, of its bond buying.
We first consider a cyclic -contraction map on a reflexive Banach space and provide a positive answer to a question raised by Al-Thagafi and Shahzad on the existence of best proximity points for cyclic -contraction maps in reflexive Banach spaces in one of their works (2009).
That's how little interest the city has in the team, which should move but is considered a leading candidate for contraction, if Commissioner Bud Selig decides to try to lop a couple of teams off the major league roster.
Recently, Ran and Reurings [20] have initiated another important direction in generalizing the Banach contraction mapping principle by considering a partial ordering on the metric space ( X, d ) and by requiring that the contraction condition (1.1) is satisfied only for comparable elements, that is, we have d ( T x, T y ) ≤ a d ( x, y ), for all x, y ∈ X, with x ≥ y. (1.3).
The loading conditions in the present simulation were similar to those of the traditional in vitro tests; thus, this study did not consider muscle contraction and complicated external load conditions [ 29].
Given a metric space, the idea of our generalization of the notion of an IFS is to consider contractions from to, rather than contractions from to itself.
A model of a bench-scale methanation reactor was set-up by modifying the classical two-phase model approach and introducing an additional bulk flow from bubble to dense phase to consider the volume contraction of the methanation reaction.
