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 $\alpha\in[\frac{1}{2}, 1)$ 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.
Mohammadi, B. (2018). Strict fixed points of \'{C}iri\'{c}-generalized weak quasicontractive multi-valued mappings of integral type. International Journal of Nonlinear Analysis and Applications, 9(2), 117-129. doi: 10.22075/ijnaa.2017.1312.1324
MLA
Babak Mohammadi. "Strict fixed points of \'{C}iri\'{c}-generalized weak quasicontractive multi-valued mappings of integral type". International Journal of Nonlinear Analysis and Applications, 9, 2, 2018, 117-129. doi: 10.22075/ijnaa.2017.1312.1324
HARVARD
Mohammadi, B. (2018). 'Strict fixed points of \'{C}iri\'{c}-generalized weak quasicontractive multi-valued mappings of integral type', International Journal of Nonlinear Analysis and Applications, 9(2), pp. 117-129. doi: 10.22075/ijnaa.2017.1312.1324
VANCOUVER
Mohammadi, B. Strict fixed points of \'{C}iri\'{c}-generalized weak quasicontractive multi-valued mappings of integral type. International Journal of Nonlinear Analysis and Applications, 2018; 9(2): 117-129. doi: 10.22075/ijnaa.2017.1312.1324
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