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

摘要

This paper discusses some convergence properties in fuzzy ordered proximal approaches defined by {(gn, Tn)}—sequences of pairs, where g:A → A is a surjective self-mapping and T:A → B,  where Aand Bare nonempty subsets of and abstract nonempty set X and (X,M,∗,≺̲) is a partially ordered non-Archimedean fuzzy metric space which is endowed with a fuzzy metric M, a triangular norm * and an ordering ≺̲. The fuzzy set M takes values in a sequence or set {Mσn} where the elements of the so-called switching rule {σn} ⊂ >Z+ are defined from X × X × >Z0+ to a subset of >Z+. Such a switching rule selects a particular realization of M at the nth iteration and it is parameterized by a growth evolution sequence {αn} and a sequence or set {ψσn} which belongs to the so-called Ψ(σ, α)-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.