Fixed point for set-valued mappings satisfying an implicit relation in partially ordered metric spaces

Beg, Ismat; Butt, Asma Rashid

doi:10.1016/j.na.2009.02.027

Cited by 109 publications

(61 citation statements)

References 15 publications

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“…After the publication of this work, several coupled fixed point and coincidence point results have appeared in the recent literature. Works noted in [3,6,7,9,11,16,17,20,21,31,32,33,34,35,36,37,41,44] are some relevant examples.…”

Section: Introductionmentioning

confidence: 99%

Coupled common fixed point results in ordered G-metric spaces

Nashine¹

2012

J. Nonlinear Sci. Appl.

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Section: Introductionmentioning

confidence: 99%

Coupled common fixed point results in ordered G-metric spaces

Nashine¹

2012

J. Nonlinear Sci. Appl.

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“…Following the publication of [20], it was natural to find a similar version of Theorem [19] to metric spaces endowed with partial order or more generally a graph. Beg and Butt [3] gave the first attempt. But their definition of multivalued monotone mappings was not correct which had the effect that the proof of their version of the fixed point theorem of Nadler was wrong (see for example [1]).…”

Section: Preliminaries and Basic Resultsmentioning

confidence: 99%

A graphical version of Reichs fixed point theorem

Alfuraidan¹,

Bachar²,

Khamsi³

2016

J. Nonlinear Sci. Appl.

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In this paper, we discuss the definition of the Reich multivalued monotone contraction mappings defined in a metric space endowed with a graph. In our investigation, we prove the existence of fixed point results for these mappings. We also introduce a vector valued Bernstein operator on the space C([0, 1], X), where X is a Banach space endowed with a partial order. Then we give an analogue to the Kelisky-Rivlin theorem.

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“…Therefore, it was natural to find an extension of Nadler's fixed point theorem to partially ordered metric spaces. Beg and Butt [3] gave the first attempt. But their definition of multivalued monotone mappings was not correct which had the effect that the proof of their version of Nadler's fixed point theorem was wrong (see for example [2]).…”

Section: H(f (X) F (Y)) ≤ K D(x Y)mentioning

confidence: 99%