We present some fixed point results for a single mapping and a pair of compatible mappings via auxiliary functions which satisfy a generalized weakly contractive condition in partially ordered complete $G$-metric spaces. Some examples are furnished to illustrate the useability of our main results. At the end, an application is presented to the study of exi...

The purpose of this paper is to prove a general fixed point theorem by altering distance for two pairs of hybrid occasionally weakly compatible mappings and to reduce the study of fixed points of pairs of mappings satisfying a contractive condition of integral type at the study of fixed point in symmetric spaces by altering distance satisfying an implicit relation.

In this work we introduce the class of weakly c-contractive mappings. We establish that these mappings necessarily have unique fixed points in complete metric spaces. We support our result by an example. Our result also generalises an existing result in metric spaces.

We prove the existence of the unique common fixed point theorems for self mappings which are weakly compatible satisfying some contractive conditions on partial metric spaces. Furthermore, we also prove the result on the continuity in the set of common fixed points for self mappings on partial metric spaces.

The present paper contains some fixed point results for weakly contractive single valued mappings on S-metric spaces and a homotopy result, which is offered as an application of the obtained new results.

We prove some common fixed point results for two pairs of weakly compatible mappings satisfying a general contractive condition without using the completeness of the space and continuity of maps.

We obtained sufficient conditions for existence of fixed points of involutions in CAT(0) spaces. Convergence results of Mann and Ishikawa iterates of weakly contractive mappings are also proved.

In this work, we establish some fixed point theorems for weakly C-contractive mappings in partial metric spaces. Presented theorems extend and generalize some existence results in the literature. Also, an example is given to support our results.

In this paper, we establish some common fixed point theorems for generalized-( ψ , α , β )-weakly contractive mappings in dislocated metric spaces. We present an example in support of our theorem.

We establish common fixed point theorems involving two pairs of weakly compatible mappings satisfying nonlinear contractive conditions in K -metric spaces. The presented theorems generalize, extend and improve many existing results in the literature. © 2011 Elsevier Ltd. All rights reserved.