De la Sen, ManuelAbbas, MujahidSaleem, Naeem2016-09-232016-09-232016-09-02De la Sen, M, Abbas, M & Saleem, N 2016, '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', SpringerPlus, vol. 5, art. #1478, pp. 1-26.2193-180110.1186/s40064-016-3116-2http://hdl.handle.net/2263/56889This 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.en© 2016 The Author(s). This article is distributed under the terms of the Creative Commons Attribution 4.0 International License.Fived pointsBest proximity pointsFuzzy setFuzzy metricOptimal fuzzy best proximity coincidence pointsProximalΨ(σ , α)-Lower-bounding mappingΨ(σ , α)-Lower-bounding asymptotically contractive mappingSwitching ruleArticle