Fixed Point Theorems on a Metric Space Endowed With an Arbitrary Binary Relation and Applications

By Bessem Samet, M. Turinici. 2012

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Discussion on Generalized-(αψ, β)-Contractive Mappings via Generalized Altering Distance Function and Related Fixed Point Theorems (2014, background): “Applications Very recently, a mapping satisfying contraction on metric spaces endowed with a binary relation has been introduced by Samet and Turinici in [17]; therefore, this work has been extended and improved in [14, 18].”
Relation-theoretic metrical coincidence theorems (2016, background): “Recently, Alam and Imdad [6] extended the classical Banach contraction principle to complete metric space endowed with a binary relation and observed that the partial order (see Nieto and Rodŕıguez-López [7]), preorder (see Turinici [8]), transitive relation (see Ben-El-Mechaiekh [9]), tolerance (”
Relation-theoretic contraction principle (2015, background): “Here, it is fascinating to point out that corresponding theorems contained in [10, 19, 2, 17, 18, 12, 11, 5, 13] cannot be used in the context of the foregoing examples (i.”
Nonlinear contractions in metric spaces under locally $T$-transitive binary relations (2015, background): “pace. A binary relation R on X is called d-self-closed if for any R-preserving sequence {xn} such that xn −→d x, there exists a subsequence {xn k } of {xn} with [xn k ,x] ∈ R ∀ k ∈ N0. Deﬁnition 2.11 [22]. Let X be a nonempty set and R a binary relation on X. A subset E of X is called R-directed if ”