# 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.

## References

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DOI 10.1186/s13663-017-0619-7.

P. Hitzler; Generalized metrics and topologies in logic programming semantics, Phd thesis, School of Mathematics, Applied Mathematics and Statistics, National University of Ireland, University College Cork (2001).

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## Published

## How to Cite

*Journal of the Nigerian Mathematical Society*,

*38*(3), 547–567. Retrieved from https://ojs.ictp.it/jnms/index.php/jnms/article/view/513