The existence of fixed points, coupled fixed points, and coupled coincidence points without the assumption of compatibility is established. The results presented in this paper extend, improve, and generalize some well-known results in the literature. Also, an example is given to show that our results are real generalizations of known ones in coupled coincidence fixed point theory. MSC: 54H25; 47H10
The main aim of this paper is to prove fixed point theorems in quasi-cone metric spaces which extend the Banach contraction mapping and others. This is achieved by introducing different kinds of Cauchy sequences in quasi-cone metric spaces.
The fixed point theorems in various contraction mappings have been provided by many researchers. Some of them used certain functions in mapping to guarantee the existence of fixed point. The purpose of this paper is to present some fixed point result on contraction mapping in partially ordered quasi-metric space that applying a w-distance. The generalized altering distance function on the mapping plays a role in theorems. The results extend some well-known results in the references. We also improve these new results to the common fixed point.
In this paper, we define almost Rg-Geraghty type contractions and utilize the same to establish some coincidence and common fixed point results in the setting of b2-metric spaces endowed with binary relations. As consequences of our newly proved results, we deduce some coincidence and common fixed point results for almost g-α-η Geraghty type contraction mappings in b2-metric spaces. In addition, we derive some coincidence and common fixed point results in partially ordered b2-metric spaces. Moreover, to show the utility of our main results, we provide an example and an application to non-linear integral equations.
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