Strict fixed points of \'{C}iri\'{c}-generalized weak quasicontractive multi-valued mappings of integral type | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 10، دوره 9، شماره 2، اسفند 2018، صفحه 117-129 اصل مقاله (386.14 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2017.1312.1324 | ||
| نویسنده | ||
| Babak Mohammadi* | ||
| Department of Mathematics, Marand Branch, Islamic Azad University, Marand, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| strict fixed point؛ '{C}iri'{c}-generalized weak quasi-contraction؛ multi-valued mappings؛ integral type | ||
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