Geodesic
Set-valued mappings: fixed point results with $\beta$-function and some applications
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 63 (2024), pp. 61-79

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Via the so-called $\beta$-function, some fixed-point results for nonexpansive set-valued mappings are obtained. In this study, the results are considered in the context of complete metric spaces which are neither uniformly convex nor compact. Our theorems extend, unify, and improve several recent results in the existing literature. In the end, we apply our new results to ensure the existence of a solution for a nonlinear integral inclusion. Moreover, we approximate the fixed point by a faster iterative process.
Keywords: fixed point, set-valued mappings, $T_{\beta}$-multivalued contractive mapping, $T_{\beta}$-weakly contractive multivalued mapping, integral inclusion, iterative process 
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     author = {Y. Touail},
     title = {Set-valued mappings: fixed point results with $\beta$-function and some applications},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {61--79},
     publisher = {mathdoc},
     volume = {63},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2024_63_a4/}
}
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Y. Touail. Set-valued mappings: fixed point results with $\beta$-function and some applications. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 63 (2024), pp. 61-79. http://geodesic.mathdoc.fr/item/IIMI_2024_63_a4/