Geodesic
Existence of best proximity points for the sum of two operators
Filomat, Tome 37 (2023) no. 23, p. 7831

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DOI

In this paper, we work on the existence of approximate solution for the fixed point equation Rx + Qx = x, when R is a weak contractive mapping and Q is a continuous self-map which is a new topic related to the background literature. Till now, no results were found to find the existence of approximate solution for such a kind of mappings in literature to the best of our knowledge. Here we prove the existence of best proximity point for the sum of a weak contractive non self map and a continuous self map. Also, we provide an example to support our main theorem. And also, we prove the existence of best proximity point for the sum of Geraghty-contraction and continuous map.
DOI : 10.2298/FIL2323831P
Classification : 47H10, 54H25
Keywords: weak contractive mapping, Geraghty-contraction map, P-property, best proximity point, compact, sum of two operators, approximately compact 
G Poonguzali; Zorana Golubović; Stojan Radenović. Existence of best proximity points for the sum of two operators. Filomat, Tome 37 (2023) no. 23, p. 7831 . doi: 10.2298/FIL2323831P
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     title = {Existence of best proximity points for the sum of two operators},
     journal = {Filomat},
     pages = {7831 },
     year = {2023},
     volume = {37},
     number = {23},
     doi = {10.2298/FIL2323831P},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2323831P/}
}
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