Geodesic
Perturbation of the fixed point problem for continuous mappings
Vestnik rossijskih universitetov. Matematika, Tome 26 (2021) no. 135, pp. 241-249

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We consider the problem of a double fixed point of pairs of continuous mappings defined on a convex closed bounded subset of a Banach space. It is shown that if one of the mappings is completely continuous and the other is continuous, then the property of the existence of fixed points is stable under contracting perturbations of the mappings. We obtain estimates for the distance from a given pair of points to double fixed points of perturbed mappings. We consider the problem of a fixed point of a completely continuous mapping on a convex closed bounded subset of a Banach space. It is shown that the property of the existence of a fixed point of a completely continuous map is stable under contracting perturbations. Estimates of the distance from a given point to a fixed point are obtained. As an application of the obtained results, the solvability of a difference equation of a special type is proved.
Keywords: double fixed point, fixed point, completely continuous mapping, continuous mapping, difference equation. 
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     author = {Z. T. Zhukovskaya and S. E. Zhukovskiy},
     title = {Perturbation of the fixed point problem for continuous mappings},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {241--249},
     publisher = {mathdoc},
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     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2021_26_135_a2/}
}
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Z. T. Zhukovskaya; S. E. Zhukovskiy. Perturbation of the fixed point problem for continuous mappings. Vestnik rossijskih universitetov. Matematika, Tome 26 (2021) no. 135, pp. 241-249. http://geodesic.mathdoc.fr/item/VTAMU_2021_26_135_a2/