The purpose of this paper is to establish some fixed point results for a class generalized $(\phi, \psi)$-weak contraction mapping in partially ordered $b$-metric space. This necessarily have unique under relation Also, the common and coincidence points self mappings are presented. These generalize extend an existing literature. Some illustrations given at end support results.

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...

By principal motivation from the results of new iterative scheme that produces faster than K-iteration. In this article, we study generalized by a iteration to approximate fixed points contraction and Suzuki non-expansive mappings. We establish strong convergence mappings closed convex Banach space also deduce data dependent results. Furthermore, prove some weak theorems in sense mapping applyi...

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.

In this paper, we modify the KF-iteration process into hyperbolic metric spaces where symmetry condition is satisfied and establish weak w2-stability data dependence results for contraction mappings. We also prove some Δ-convergence strong convergence theorems generalized (α,β)-nonexpansive type 1 Finally, offer a numerical example of mappings show that more effective than other iterations. Our...

In this manuscript, common fixed point results for set-valued mapping under generalized ψ , ϕ 1 and id="M2"> 2 weak contraction without using Hausdorff metric are studied endowing with a graph. To demo...

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...