NEW FIXED POINT THEOREMS IN DISLOCATED METRIC SPACES
Abstract
In this paper, the notion of dislocated metric space, which is a proper generalization of the notion of metric space is discussed. A new class of contractive mappings on dislocated metric space, called the class of 3 $\alpha$-contractive mappings is introduced. Using some classical results, new fixed point theorems are established in dislocated metric spaces for the class of 3$\alpha$-contractive mappings. Concrete examples and an application of our theorems to establishment of existence of solutionof certain two-point boundary value problem are given. As further findings of this research, certain anomalies detected in the existing literature are corrected.
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