F-closed sets and coupled fixed point theorems without the mixed monotone property

Kutbi, Marwan Amin; Roldán, Antonio; Sintunavarat, Wutiphol; Martínez-Moreno, Juan; Roldán, Concepción

doi:10.1186/1687-1812-2013-330

Cited by 17 publications

(12 citation statements)

References 17 publications

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“…Motivated by the notion of F-invariant subset of X 6 (for the mapping F : X 3 → X) due to Charoensawan [48] and the notion of F-closed subset of X 4 (for the mapping F : X 2 → X) due to Kutbi et al [49], Alam and Imdad [16] introduced the following. Here it can be pointed out that instead of saying that f is R-continuous, Roldán-López-de-Hierro et al [17], Shahzad et al [19] and Roldán-López-de-Hierro and Shahzad [18] said that f is (d, R)-nondecreasingcontinuous.…”

Section: Relation-theoretic Notions and Auxiliary Resultsmentioning

confidence: 99%

Relation-theoretic metrical coincidence theorems

Alam

Imdad

2017

Filomat

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In this article, we generalize some frequently used metrical notions such as: completeness, closedness, continuity, -continuity and compatibility to relation-theoretic setting and utilize these relatively weaker notions to prove our results on the existence and uniqueness of coincidence points involving a pair of mappings defined on a metric space endowed with an arbitrary binary relation. Particularly, under universal relation our results deduce the classical coincidence point theorems of Goebel, Jungck and others. Furthermore, our results generalize, modify, unify and extend several well-known results of the existing literature.

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Section: Relation-theoretic Notions and Auxiliary Resultsmentioning

confidence: 99%

Relation-theoretic metrical coincidence theorems

Alam

Imdad

2017

Filomat

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“…The following definition is a variant of the notion of F -invariant subset of X 6 (for the mapping F : X 3 → X) introduced by Charoensawan [3] and the notion of F -closed subset of X 4 (for the mapping F : X 2 → X) introduced by Kutbi et al [7] to the mapping T : X → X.…”

Section: Definition 24 (Seementioning

confidence: 98%

Relation-theoretic contraction principle

Alam

Imdad

2015

J. Fixed Point Theory Appl.

147

191

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In this paper, we present yet another new and novel variant of classical Banach contraction principle on a complete metric space endowed with a binary relation which, under universal relation, reduces to Banach contraction principle. In process, we observe that various kinds of binary relations, such as partial order, preorder, transitive relation, tolerance, strict order, symmetric closure, etc., utilized by earlier authors in several well-known metrical fixed point theorems can be weakened to the extent of an arbitrary binary relation.Mathematics Subject Classification. 47H10, 54H25.

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“…In 2012, Sintunaravat et al [16] introduced the notion of transitive property and utilized the same to extend some Samet-Vetro coupled fixed point theorems for nonlinear contractions. On the other hand, Kutbi et al [12] weakened the notion of F -invariant sets by introducing the notion of F -closed sets. Recently, Karapinar et al [13] proved some unidimensional versions of earlier coupled fixed point results involving F -closed sets and then obtained such coupled fixed point results as easy by using their corresponding (unidimensional) fixed point results.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear contractions in metric spaces under locally T-transitive binary relations

Alam¹,

Imdad²

2018

FPT-RO

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Abstract. In this paper, we present a variant of Boyd-Wong fixed point theorem in a metric space equipped with a locally T -transitive binary relation, which under universal relation reduces to Boyd-Wong (Proc. Amer. Math. Soc. 20(1969), 458-464) and Jotic (Indian J. Pure Appl. Math. 26(1995), 947-952) fixed point theorems. Also, our results extend several other well-known fixed point theorems such as: Alam and Imdad (J. Fixed Point Theory Appl. 17(2015), no 4, 693-702) and Karapinar and Roldán-López-de-Hierro (J. Inequal. Appl. 2014Appl. :522(2014, 12 pages) besides some others.

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F-closed sets and coupled fixed point theorems without the mixed monotone property

Cited by 17 publications

References 17 publications

Relation-theoretic metrical coincidence theorems

Relation-theoretic metrical coincidence theorems

Relation-theoretic contraction principle

Nonlinear contractions in metric spaces under locally T-transitive binary relations

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