On optimal fuzzy best proximity coincidence points of fuzzy order preserving proximal Ψ(σ, α)-lower-bounding asymptotically contractive mappings in non-Archimedean fuzzy metric spaces

This paper discusses some convergence properties in fuzzy ordered proximal approaches defined by $\{(g_n,T_n)\}$—sequences of pairs, where $g:A\to A$ is a surjective self-mapping and $T:A\to B,$ where Aand Bare nonempty subsets of and abstract nonempty set X and $(X,M,\ast ,\underline{\prec })$ is a partially ordered non-Archimedean fuzzy metric space which is endowed with a fuzzy metric M, a triangular norm * and an ordering $\underline{\prec }.$ The fuzzy set M takes values in a sequence or set $\{M_{{\mathit{\sigma }}_n}\}$ where the elements of the so-called switching rule $\{{\mathit{\sigma }}_n\}\subset {\mathit{Z}}_{+}$ are defined from $X\times X\times {\mathit{Z}}_{0+}$ to a subset of ${\mathit{Z}}_{+}.$ Such a switching rule selects a particular realization of M at the nth iteration and it is parameterized by a growth evolution sequence $\{{\mathit{\alpha }}_n\}$ and a sequence or set $\{{\mathit{\psi }}_{{\mathit{\sigma }}_n}\}$ which belongs to the so-called $\mathit{\Psi }(\mathit{\sigma },\mathit{\alpha })$-lower-bounding mappings which are defined from [0, 1] to [0, 1]. Some application examples concerning discrete systems under switching rules and best approximation solvability of algebraic equations are discussed.