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}⊂ZZ+ are defined from X×X×ZZ0+ to a subset of ZZ+. 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.
