Geodesic
Best proximity point theorems for proximal multi-valued contractions
Filomat, Tome 35 (2021) no. 6, p. 1889

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DOI

In this paper, we introduce new classes of proximal multi-valued contractions in a metric space and proximal multi-valued nonexpansive mappings in a Banach space and show the existence of best proximity points for both classes. Further, for proximal multi-valued nonexpansive mappings, we prove a best proximity point theorem on starshape sets. As a consequence, we also obtain some new fixed point theorems. Finally, we give some examples to illustrate our main results.
DOI : 10.2298/FIL2106889B
Classification : 47H09, 47H10, 54H25
Keywords: Best proximity point, fixed point, proximal multi-valued contraction, proximal multivalued nonexpansive mapping, starshaped set 
Nuttawut Bunlue; Yeol Je Cho; Suthep Suantai. Best proximity point theorems for proximal multi-valued contractions. Filomat, Tome 35 (2021) no. 6, p. 1889 . doi: 10.2298/FIL2106889B
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     title = {Best proximity point theorems for proximal multi-valued contractions},
     journal = {Filomat},
     pages = {1889 },
     year = {2021},
     volume = {35},
     number = {6},
     doi = {10.2298/FIL2106889B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2106889B/}
}
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