title: On optimal fuzzy best proximity coincidence points of fuzzy order preserving proximalΨ(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, whereg:A→Ais a surjective self-mapping andT:A→B,whereAandBare nonempty subsets of and abstract nonempty setXand(X,M,∗,≺̲)is a partially ordered non-Archimedean fuzzy metric space which is endowed with a fuzzy metricM, a triangular norm * and an ordering≺̲.The fuzzy setMtakes values in a sequence or set{Mσn}where the elements of the so-called switching rule{σn}⊂Z+are defined fromX×X×Z0+to a subset ofZ+.Such a switching rule selects a particular realization ofMat thenth iteration and it is parameterized by a growth evolution sequence{αn}and a sequence or set{ψσn}which belongs to the so-calledΨ(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.
authors.affiliation: Faculty of Science and Technology, Institute of Research and Development of Processes IIDP, University of the Basque Country, Barrio Sarriena, P.O. Box 644 de Bilbao, 48940 Leioa, Bizkaia Spain.
authors.forename: Manuel
authors.initials: M
authors.lastname: De la Sen
authors.affiliation: Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jidda, 21589 Saudi Arabia.|Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood Road, Pretoria, 0002 South Africa.
authors.forename: Mujahid
authors.initials: M
authors.lastname: Abbas
authors.affiliation: Department of Mathematics, National University of Computer and Emerging Sciences, Milaad Street, Lahore, 54000 Pakistan.|Department of Mathematics, University of Management and Technology, C-II Johar Town, Lahore, Pakistan.
authors.forename: Naeem
authors.initials: N
authors.lastname: Saleem
keywords: Best proximity points; Fixed points; Fuzzy metric; Fuzzy set; Optimal fuzzy best proximity coincidence points; Proximal; Switching rule