Geodesic
Fixed point theorem for question of set-valued quasi-contraction
Filomat, Tome 36 (2022) no. 19, p. 6777

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DOI

In this work, we give a partial positive answer to the question concerning the set-valued quasi-contraction proposed by Amini-Harandi (Appl. Math. Lett. 24:1791–1794 2011). By a useful lemma, we prove a fixed point theorem for the set-valued quasi-contraction, which extends the range of contraction constant in result of Amini-Harandi from 0, 1 2 to 0, 1 3 √ 3. Also, we give a new simple proof for the result of quasi-contraction type proposed by Haghi et al. (Appl. Math. Lett. 25:843–846 2012). Finally, a counterexample and a theorem concerning cyclic set-valued mapping are given, which improve some recent results.
DOI : 10.2298/FIL2219777L
Classification : 47H10, 54H25
Keywords: set-valued, quasi-contraction, quasi-contraction type, weak contraction, cyclic mapping 
Ning Lu; Fei He; Shu-Fang Li. Fixed point theorem for question of set-valued quasi-contraction. Filomat, Tome 36 (2022) no. 19, p. 6777 . doi: 10.2298/FIL2219777L
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     title = {Fixed point theorem for question of set-valued quasi-contraction},
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     doi = {10.2298/FIL2219777L},
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     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2219777L/}
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