Open AccessBest proximity point theorems for proximal multi-valued contractions
Author(s) -
Nuttawut Bunlue,
Yeol Cho Je,
Suthep Suantai
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2106889b
Subject(s) - mathematics , metric space , banach space , fixed point theorem , point (geometry) , complete metric space , space (punctuation) , discrete mathematics , pure mathematics , fixed point , mathematical analysis , geometry , computer science , operating system
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.