The Banach contraction principle is one of the pivotal results in the metric fixed-point theory. It is a popular tool for the solution of existence problems in various fields of mathematics. There are several generalizations of the Banach contraction principle in the related literature on the metric fixed-point theory. Ran and Reurings [15] extended the Banach contraction principle in partially...

recently, zhang and song [q. zhang, y. song, fixed point theory forgeneralized $varphi$-weak contractions,appl. math. lett. 22(2009) 75-78] proved a common fixed point theorem for two mapssatisfying generalized $varphi$-weak contractions. in this paper, we prove a common fixed point theorem fora family of compatible maps. in fact, a new generalization of zhangand song's theorem is given.

Dynamic doxastic logic concerns an agent who inhabits a world and is able to form theories about it. In particular there are three types of doxastic action of which he is capable: expanding his beliefs by accepting a proposition φ without modifying the resulting set of beliefs; revising his beliefs by accepting a proposition φ and modifying the resulting set of beliefs; and contracting his beli...

For abstract operator spaces V and W , a linear map φ : V → W provides another linear map φn : Mn(A) → Mn(B) defined by φn((ai,j)) = (φ(ai,j)) where n = 1, 2, ···. If a sequence {‖φn‖} ∞ n=1 belongs to l , then φ is said to be a completely bounded map. W. Stinespring [7] and W. Arveson [1] started operator space theory related to complete boundedness for a map φ : S → B(K) where S ⊂ B(H) and H ...

We study the extent to which properties of infinite-dimensional dynamical systems can be accurately detected by examining observations of such systems. Let H be a separable Hilbert space. Let f : H → H be a map and let A ⊂ H be a compact set satisfying f(A) = A. We prove that for almost every (in the sense of prevalence) continuous observable φ : H → RM , if f induces a map f̄ satisfying f̄ ◦ φ =...

In this paper, we will provide some examples of Banach spaces that are Gâteaux differentiability spaces but not weak Asplund, weak Asplund but not in class(
̃), in class(
̃) but whose dual space is not weak∗ fragmentable. We begin with some definitions. A Banach space X is called a weak Asplund space [almost weak Asplund] (Gâteaux differentiability space) if each continuous convex function define...

In this paper, the notion of $psi -$weak contraction cite{Rhoades} isextended to fuzzy metric spaces. The existence of common fixed points fortwo mappings is established where one mapping is $psi -$weak contractionwith respect to another mapping on a fuzzy metric space. Our resultgeneralizes a result of Gregori and Sapena cite{Gregori}.

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...

A compatible point-shift f maps, in a translation invariant way, each point of a stationary point process Φ to some point of Φ. It is fully determined by its associated point-map, gf , which gives the image of the origin by f . The initial question of this paper is whether there exist probability measures which are left invariant by the translation of −gf . The point-map probabilities of Φ are ...