Abstract
The aim of this paper is to define the new type of mappings which is called a weak \(\psi \)-\(\phi \)-contraction mapping. Fixed point theorems for such mappings in partial metric spaces are established. Moreover, we present an example and numerical result for the main result. By providing this example, we show that our main result is a real generalization of the fixed point results of several mathematicians in the literature. As an application, we apply our results to prove the existence theorems of best proximity points for the non-self mappings.
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The second author would like to thank the Thailand Research Fund and Office of the Higher Education Commission under grant no. MRG5980242 for financial support during the preparation of this manuscript.
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Ninsri, A., Sintunavarat, W. Toward a generalized contractive condition in partial metric spaces with the existence results of fixed points and best proximity points. J. Fixed Point Theory Appl. 20, 13 (2018). https://doi.org/10.1007/s11784-018-0499-4
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DOI: https://doi.org/10.1007/s11784-018-0499-4