Geodesic
Implicit Function Theorems for Continuous Mappings
Matematičeskie zametki, Tome 113 (2023) no. 6, pp. 793-806

Voir la notice de l'article provenant de la source Math-Net.Ru

Local and nonlocal implicit function theorems are obtained for closed mappings with a parameter from one Asplund space to another. These theorems are formulated in terms of the regular coderivative of a mapping at a point. The obtained results are applied to study properties of the minimum function for a constrained extremum problem with equality-type constraints and with a parameter. Sufficient conditions for the upper semicontinuity of the minimum function for a given parameter value are obtained.
Keywords: implicit function, regular coderivative, minimum function. 
@article{MZM_2023_113_6_a0,
     author = {A. V. Arutyunov and S. E. Zhukovskiy and B. Sh. Mordukhovich},
     title = {Implicit {Function} {Theorems} for {Continuous} {Mappings}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {793--806},
     publisher = {mathdoc},
     volume = {113},
     number = {6},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_113_6_a0/}
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A. V. Arutyunov; S. E. Zhukovskiy; B. Sh. Mordukhovich. Implicit Function Theorems for Continuous Mappings. Matematičeskie zametki, Tome 113 (2023) no. 6, pp. 793-806. http://geodesic.mathdoc.fr/item/MZM_2023_113_6_a0/