2016
DOI: 10.1186/s13663-016-0534-3
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Abstract: In this paper, we introduce best proximal contractions in complete ordered non-Archimedean fuzzy metric space and obtain some proximal results. The obtained results unify, extend, and generalize some comparable results in the existing literature. MSC: 47H10; 47H04; 47H07

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Cited by 15 publications
(20 citation statements)
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“…Definition 2.1 ( [1,22]). Let A be a nonempty subset of a non-Archimedean fuzzy metric space (X, M, * ).…”
Section: Completeness Resultsmentioning
confidence: 99%
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“…Definition 2.1 ( [1,22]). Let A be a nonempty subset of a non-Archimedean fuzzy metric space (X, M, * ).…”
Section: Completeness Resultsmentioning
confidence: 99%
“…Definition 2.4 ( [1,22]). A set B is said to be fuzzy approximatively compact with respect to A if for every sequence {y n } in B and for some x ∈ A, M (x, y n , t) −→ M (x, B, t) implies that x ∈ A 0 (t).…”
Section: Completeness Resultsmentioning
confidence: 99%
See 1 more Smart Citation
“…In this context, Definition 6 can be applied to the partially order preserving non-Archimedean fuzzy metric space (X, M , * , ≺) (i.e., (X , ≺) is a partially order preserving set and (X, M , * ) is a non-Archimedean fuzzy metric space, [38]) to a p-cyclic mapping T : ∪ i∈p X i → ∪ i∈p X i where X i ⊆ Xare non-empty sets; ∀i ∈ p.…”
Section: Remarkmentioning
confidence: 99%
“…There are also abundant studies on all such topics in classical metric spaces and Banach spaces, either in the fuzzy formalism or not necessarily under the fuzzy formalism, including a lot of research on contractive and non-expansive mappings, self-mappings and, in particular, cyclic proximal mappings. (See, for instance, [26][27][28][29][38][39][40][41][42][43] and the references therein concerning different iterative schemes and their relations to proximal split feasibility, variational inequalities and fixed point problems. There are also recent studies on the generalizations of several types of contractions in [31] with an introduction of the so-called simulation function.…”
Section: Introductionmentioning
confidence: 99%