Coincidence, fixed points in symmetric $ (q_1,q_2) $-quasi-metric spaces and sensitivity analysis of generalized equations

Nguyen Huu Tron; Michel A. Théra

doi:10.3934/jdg.2025012

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2026, Volume 14: 36-63. Doi: 10.3934/jdg.2025012

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Coincidence, fixed points in symmetric $ (q_1,q_2) $-quasi-metric spaces and sensitivity analysis of generalized equations

Nguyen Huu Tron^1, and
Michel A. Théra^{1, 2, ,}

1.
Department of Mathematics and Statistics, Quy Nhon University, 170 An Duong Vuong, Quy Nhon, Binh Dinh, Vietnam
2.
XLIM UMR-CNRS 7252, Université de Limoges, Limoges, France

^*Corresponding author: Michel A. Théra
^*Corresponding author: Michel A. Théra

Received: December 2024

Revised: March 2025

Early access: April 9, 2025

Published online: April 9, 2025

The first author is supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.01-2023.44. The second author benefited from the support of the FMJH Program Gaspard Monge for optimization and operations research and their interactions with data science.

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Abstract

The current paper addresses non-local results on approximate and fixed points theorems for set-valued mappings in the context of symmetric $ (q_1, q_2) $-quasi-metric spaces, considering the regularity of the mappings involved. From these results, we derive non-local coincidence and double fixed point theorems for a pair of set-valued mappings, as well as non-local (Hölder) approximate, Milyutin, and Lyusternik-Graves theorems, along with (Hölder) approximate and implicit multifunction theorems in the same context. Our results extend those recently presented in the literature [1,25,23,2,26], which encompass classical results such as Nadler's multi-valued fixed point theorem [22] and Dontchev-Rockafellar's fixed point theorem [11].

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Mathematics Subject Classification: Primary: 49J52, 49J53; Secondary: 90C30.

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References

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