Geodesic
The Existence of Zeros of Multivalued Functionals, Coincidence Points, and Fixed Points in~$f$-Quasimetric Spaces
Matematičeskie zametki, Tome 110 (2021) no. 4, pp. 598-609

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

The notion of a $\lambda$-generalized-search multivalued functional on an $f$-quasimetric space is introduced. An existence theorem for zeros of such functionals is proved. As corollaries, theorems on coincidence and fixed points of multivalued mappings of $f$-quasimetric spaces are proved. In particular, Nadler's well-known theorem on fixed points of multivalued contraction mappings is generalized to the case of an $f$-quasimetric space. For a large class of single-valued mappings, including generalized contractions, a theorem on the existence of a (not necessarily unique) fixed point is proved. This theorem extends the existence part of E. S. Zhukovskii's recent fixed-point theorem for generalized contractions, which is a generalization to $f$-quasimetric spaces of Krasnosel'skii's well-known fixed-point theorem and Browder's fixed-point theorem (equivalent to Krasnosel'skii's theorem).
Mots-clés : $f$-quasimetric space
Keywords: $\lambda$-generalized-search functional, coincidence point, fixed point, generalized contraction. 
@article{MZM_2021_110_4_a10,
     author = {T. N. Fomenko},
     title = {The {Existence} of {Zeros} of {Multivalued} {Functionals,} {Coincidence} {Points,} and {Fixed} {Points} in~$f${-Quasimetric} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {598--609},
     publisher = {mathdoc},
     volume = {110},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_110_4_a10/}
}
TY  - JOUR
AU  - T. N. Fomenko
TI  - The Existence of Zeros of Multivalued Functionals, Coincidence Points, and Fixed Points in~$f$-Quasimetric Spaces
JO  - Matematičeskie zametki
PY  - 2021
SP  - 598
EP  - 609
VL  - 110
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2021_110_4_a10/
LA  - ru
ID  - MZM_2021_110_4_a10
ER  - 
%0 Journal Article
%A T. N. Fomenko
%T The Existence of Zeros of Multivalued Functionals, Coincidence Points, and Fixed Points in~$f$-Quasimetric Spaces
%J Matematičeskie zametki
%D 2021
%P 598-609
%V 110
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2021_110_4_a10/
%G ru
%F MZM_2021_110_4_a10
T. N. Fomenko. The Existence of Zeros of Multivalued Functionals, Coincidence Points, and Fixed Points in~$f$-Quasimetric Spaces. Matematičeskie zametki, Tome 110 (2021) no. 4, pp. 598-609. http://geodesic.mathdoc.fr/item/MZM_2021_110_4_a10/