Abstract
Recently, Altun et al. [1] introduced the notion of p-proximal contractions and p-proximal contractive mappings and discussed about best proximity point results for this two classes of mappings. After that, Gabeleh and Markin [3] showed that the best proximity point theorem for p-proximal contractions proved in [1] follows from the same conclusion fixed point theory. In this short note, we show that the best proximity point theorem for p-proximal contractive mappings follows from the corresponding fixed point result for metric spaces.
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References
I. Altun, M. Aslantas and H. Sahin, Best proximity point results for p-proximal contractions, Acta Math. Hungar., 162 (2020), 393–402.
I. Altun, G. Durmaz and M. Olgun, P-contractive mappings on metric spaces, J. Nonlinear Funct. Anal., 2018 (2018) 1–7.
M. Gabeleh and J. Markin, A note on the paper “Best proximity point results for p-proximal contractions,” Acta Math. Hungar., 164 (2021), 326–329.
S. Som, A remark on the paper “A note on the paper Best proximity point results for p-proximal contractions,” Acta Math. Hungar., 166 (2022), 103–106.
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I thank the referee for giving several constructive suggestions which have improved the presentation of the paper.
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Som, S. Comments on the paper “Best proximity point results for p-proximal contractions”. Acta Math. Hungar. 168, 516–519 (2022). https://doi.org/10.1007/s10474-022-01287-2
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DOI: https://doi.org/10.1007/s10474-022-01287-2