A best proximity point theorem for Geraghty-contractions

Caballero, J.; Harjani, J.; Sadarangani, Kishin

doi:10.1186/1687-1812-2012-231

Cited by 58 publications

(39 citation statements)

References 9 publications

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“…Finally, we recall the following result of Caballero et al [17]. Recently, Kumam et al [18] introduced the useful notion of triangular α-proximal admissible mapping as follows.…”

Section: Definitionmentioning

confidence: 95%

Best Proximity Point Results in Non-Archimedean Modular Metric Space

Paknazar

Sen²

2017

Mathematics

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Abstract:In this paper, we introduce the new notion of Suzuki-type (α, β, θ, γ)-contractive mapping and investigate the existence and uniqueness of the best proximity point for such mappings in non-Archimedean modular metric space using the weak P λ -property. Meanwhile, we present an illustrative example to emphasize the realized improvements. These obtained results extend and improve certain well-known results in the literature.

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“…Finally, we recall the following result of Caballero et al [17]. Recently, Kumam et al [18] introduced the useful notion of triangular α-proximal admissible mapping as follows.…”

Section: Definitionmentioning

confidence: 95%

Best Proximity Point Results in Non-Archimedean Modular Metric Space

Paknazar

Sen²

2017

Mathematics

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“…This result is of particular interest since many real world problems can be identified in a partially ordered complete metric space. Cabellero et al [8] discussed the existence of a best proximity point of Geraghty contraction. The references [5,10,11,25,[27][28][29][30] furnish some appealing best proximity point theorems for various contractions while Basha [23] and Shahzad [26] explore some common best proximity point theorems for certain contractions.…”

Section: Introductionmentioning

confidence: 99%

Coincidence best proximity points for geraghty type proximal cyclic contractions

Komal¹,

Hussain²,

Sultana³

2018

J. Math. Computer Sci.

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In this paper, we study the notions of generalized Geraghty proximal cyclic contractions for non-self mapping and obtain coincidence best proximity point theorems in the framework of complete metric spaces. Some examples are given to show the validity of our results. Our results extended and unify many existing results in the literature.Keywords: α-Geraghty proximal contraction of first and second kind, α-proximal cyclic contraction, α-proximal admissible maps.

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“…It is know that BCP has been extended in many various directions by several authors, see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and the references therein. The following generalization is due to Geraghty [7].…”

Section: Introductionmentioning

confidence: 99%