ABSTRACT. We prove some common fixed point results for four mappings satisfying generalized weak contractive condition in partially ordered complete b-metric spaces. Our results extend and improve several comparable results in the existing literature

In this paper, we introduce a modified version of ordered partial b-metric spaces. We demonstrate a fundamental lemma for the convergence of sequences in such spaces. Using this lemma, we prove some fixed point and common fixed point results for (ψ , ϕ)-weakly contractive mappings in the setup of ordered partial b-metric spaces.Finally, examples are presented to verify the effectiveness and applicability of our main results. MSC: 47H10; 54H25

We first introduce a new concept of b-dislocated metric space as a generalization of dislocated metric space and analyze different properties of such spaces. A fundamental result for the convergence of sequences in b-dislocated metric spaces is established and is employed to prove some common fixed point results for four mappings satisfying the generalized weak contractive condition in partially ordered b-dislocated metric spaces. Moreover, some examples and applications to integral equations are given here to illustrate the usability of the obtained results.

In this work, the class of b-rectangular metric spaces is introduced, some fixed point results dealing with rational type contractions and almost generalized weakly contractive mappings are obtained. Certain examples are given to support the results.

The aim of this paper is to present some common fixed point theorems for g-weakly isotone increasing mappings satisfying a generalized contractive type condition under a continuous function in the framework of ordered b-metric spaces. Our results extend the results of Nashine et al. [H. K. Nashine, B. Samet, C. Vetro, Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces, Math. Comput. Modelling 54 (2011) 712-720] from the context of ordered metric spaces to the setting of ordered b-metric spaces. Moreover, some examples of applications of the main result are given. Finally, we establish an existence theorem for a solution of an integral equation.