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.
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Date
2016-09-02
Journal Title
Journal ISSN
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Publisher
Springer Plus
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 socalled 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.
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Keywords
Mathematics, Fixed points, Best proximity points, Fuzzy set, Fuzzy metric, Optimal fuzzy best proximity coincidence points, Proximal, Ψ (σ, α)-Lower-bounding mapping, Ψ (σ, α)-Lower-bounding asymptotically contractive mapping, Switching rule.
Citation
Sen, M. D. l., 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. Springer Plus, 5(1478), 1-26. (Naeem Saleem (Mathematics /SSC), JCR LISTED (IF:0.982))