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

Abstract

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.