Geodesic
Equivalence between best proximity point and fixed point for some class of multi-valued mappings
Mandal, M.1 ; Som, S.2
1 Department of Mathematics‎, ‎School of Basic and Applied Sciences, ‎Adamas University, ‎Barasat-700126, India
2 Department of Mathematics‎, ‎School of Basic and Applied Sciences, ‎Adamas University, ‎Barasat-700126, India;Mathematics Division‎, ‎School of Advanced Sciences and Languages, ‎VIT Bhopal University, ‎Madhya Pradesh-466114, India
Journal of nonlinear sciences and its applications, Tome 17 (2024) no. 3, p. 123-127.

Voir la notice de l'article provenant de la source International Scientific Research Publications

‎In the year 2016‎, ‎Pragadeeswarar et al‎. ‎[V‎. ‎Pragadeeswarar‎, ‎M‎. ‎Marudai‎, ‎P‎. ‎Kumam‎, ‎J‎. ‎Nonlinear Sci‎. ‎Appl.‎, ‎${\bf 9}$ (2016)‎, ‎1911--1921] considered a special class of multi-valued mappings and investigated the existence of best proximity points for such class of mappings which generalizes the fixed point result established by Choudhury et al‎. ‎[B‎. ‎S‎. ‎Choudhury‎, ‎N‎. ‎Metiya‎, ‎Arab J‎. ‎Math‎. ‎Sci.‎, $‎{\bf 17}$ (2011)‎, ‎135--151] in the context of partially ordered metric spaces‎. ‎In this note‎, ‎we have showed that the best proximity point result is a direct consequence of the corresponding fixed point result‎. ‎In the last part of this note‎, ‎we applied our result in [V‎. ‎Pragadeeswarar‎, ‎M‎. ‎Marudai‎, ‎P‎. ‎Kumam‎, ‎J‎. ‎Nonlinear Sci‎. ‎Appl.‎, ‎${\bf 9}$ (2016)‎, ‎1911--1921‎, ‎Example 2.2] to validate our claim‎.
DOI : 10.22436/jnsa.017.03.02
Classification : 47H10, 54H25
Keywords: Best proximity point, multi-valued mapping, partially ordered metric space, fixed point‎

Mandal, M. 1 ; Som, S. 2

1 Department of Mathematics‎, ‎School of Basic and Applied Sciences, ‎Adamas University, ‎Barasat-700126, India
2 Department of Mathematics‎, ‎School of Basic and Applied Sciences, ‎Adamas University, ‎Barasat-700126, India;Mathematics Division‎, ‎School of Advanced Sciences and Languages, ‎VIT Bhopal University, ‎Madhya Pradesh-466114, India 
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Mandal, M.; Som, S. Equivalence between best proximity point and fixed point for some class of multi-valued mappings. Journal of nonlinear sciences and its applications, Tome 17 (2024) no. 3, p. 123-127. doi : 10.22436/jnsa.017.03.02. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.017.03.02/

[1] Banach, S. Sur les op´erations dans les ensembles abstraits et leur application aux ´equations int´egrales, Fund. Math., Volume 3 (1922), pp. 133-181 | DOI

[2] Choudhury, B. S.; Metiya, N. Multivalued and singlevalued fixed point results in partially ordered metric spaces, Arab J. Math. Sci., Volume 17 (2011), pp. 135-151 | Zbl | DOI

[3] Jain, S. K.; Meena, G.; Singh, D.; Maitra, J. K. Best proximity point results with their consequences and applications, J. Inequal. Appl., Volume 2022 (2022), pp. 1-16 | Zbl | DOI

[4] Pragadeeswarar, V.; Marudai, M.; Kumam, P. Best proximity point theorems for multivalued mappings on partially ordered metric spaces, J. Nonlinear Sci. Appl., Volume 9 (2016), pp. 1911-1921

[5] Som, S.; Gabeleh, M. Comments on the paper “Best proximity point results with their consequences and applications”, J. Inequal. Appl., Volume 2022 (2022), pp. 1-9 | DOI | Zbl

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