Abstract
Very recently, I. Altun, M. Aslantas and H. Sahin [1] introduced the notion of \(p\)-proximal contractions and surveyed the existence of best proximity points for such class of non-self mappings in metric spaces. In this note we show that this existence result is a straightforward consequence of the same conclusion in fixed point theory.
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References
Altun, I., Aslantas, M., Sahin, H.: Best proximity point results for \(p\)-proximal contractions. Acta Math. Hungar. 162, 393–402 (2020)
Fernández-León, A.: Best proximity points for proximal contractions. J. Nonlinear Convex Anal. 15, 313–324 (2014)
O. Popescu, A new type of contractive mappings in complete metric spaces, preprint
S. Sadiq Basha, Best proximity points: optimal solutions, J. Optim. Theory Appl., 151 (2011), 210–216
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The authors are thankful to the referee for making valuable suggestions leading to a better presentation of the paper.
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The first author was partially supported by a grant from Ayatollah Boroujerdi University.
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Gabeleh, M., Markin, J. A note on the paper ``Best proximity point results for \(p\)-proximal contractions". Acta Math. Hungar. 164, 326–329 (2021). https://doi.org/10.1007/s10474-021-01139-5
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DOI: https://doi.org/10.1007/s10474-021-01139-5