Strict fixed points of '{C}iri'{c}-generalized weak quasicontractive multi-valued mappings of integral type
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Abstract:
Many authors such as Amini-Harandi, Rezapour et al., Kadelburg et al., have tried to find at least one fixed point for quasi-contractions when $alphain[frac{1}{2}, 1)$ but no clear answer exists right now and many of them either have failed or changed to a lighter version. In this paper, we introduce some new strict fixed point results in the set of multi-valued '{C}iri'{c}-generalized weak quasi-contraction mappings of integral type. We consider a necessary and sufficient condition on such mappings which guarantees the existence of unique strict fixed point of such mappings. Our result is a partial positive answer for the mentioned problem which has remained open for many years. Also, we give an strict fixed point result of $alpha$-$psi$-quasicontractive multi-valued mappings of integral type. Our results generalize and improve many existing results on multi-valued mappings in literature. Moreover, some examples are presented to support our new class of multi-valued contractions.
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Journal title
volume 9 issue 2
pages 117- 129
publication date 2018-12-15
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