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Remarks on the paper "Best proximity point theorem in higher dimensions with an application" | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 25، دوره 14، شماره 4، تیر 2023، صفحه 333-336 اصل مقاله (311.01 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.27496.3623 | ||
| نویسندگان | ||
| Sumit Som1؛ Moosa Gabeleh* 2 | ||
| 1Department of Mathematics, School of Basic and Applied Sciences, Adamas University, Barasat-700126, India | ||
| 2Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran | ||
| تاریخ دریافت: 24 خرداد 1401، تاریخ بازنگری: 09 تیر 1401، تاریخ پذیرش: 28 مرداد 1401 | ||
| چکیده | ||
| Very recently S. Mondal et al. [Best proximity point theorem in higher dimensions with an application, Int. J. Nonlinear Anal. Appl. (2022) ] introduced the concept of $F_n$-contractions ($n\geq 2$) and investigated the existence and uniqueness of an $n$-tuple best proximity point for this class of mappings in the framework of metric spaces. In this paper, we prove that their main result is a straightforward consequence of the Banach contraction principle. | ||
| کلیدواژه‌ها | ||
| Best proximity point؛ $F_n$-contraction؛ weak $P$-property؛ $n$-tupled fixed point؛ $n$-tupled best proximity point | ||
| مراجع | ||
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[1] S. Banach, Sur les operations dans les ensembles abstraits et leur applications aux equations integrals, Fund. Math. 3 (1922), 133—181. [2] M. Gabeleh, Global optimal solutions of non-self mappings, Sci. Bull.‘Politeh.’Univ. Buchar. Ser. A. 75 (2013), 67–74. [3] M. Gabeleh and O.O. Otafudu, Markov–Kakutani’s theorem for best proximity pairs in Hadamard spaces, Indag. Math. 28 (2017), 680–693. [4] S. Mondal, S. Lahal and A. Chanda, Best proximity point theorem in higher dimensions with an application, Int. J. Nonlinear Anal. Appl. 13 (2022), no. Special Issu, 97–10 | ||
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