Coincidence, fixed points in symmetric <inline-formula><tex-math id="M1">$ (q_1,q_2) $</tex-math></inline-formula>-quasi-metric spaces and sensitivity analysis of generalized equations

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].