A Note on Some Best Proximity Point Theorems Proved underP-Property

In the very recent paper of Akbar and Gabeleh (2013), by using the notion ofP-property, it was proved that some late results about the existence and uniqueness of best proximity points can be obtained from the versions of associated existing results in the fixed point theory. Along the same line, in this paper, we prove that these results can be obtained under a weaker condition, namely, weakP-property.

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On Best Proximity Points under the -Property on Partially Ordered Metric Spaces

Abstract and Applied Analysis ◽

10.1155/2013/150970 ◽

2013 ◽

Vol 2013 ◽

pp. 1-6 ◽

Cited By ~ 1

Author(s):

Mohamed Jleli ◽

Erdal Karapinar ◽

Bessem Samet

Keyword(s):

Fixed Point ◽

Partial Order ◽

Metric Space ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Fixed Point Theory ◽

Best Proximity Point ◽

Point Theory ◽

Point Of View ◽

Ordered Metric Spaces

Very recently, Abkar and Gabeleh (2013) observed that some best proximity point results under the -property can be obtained from the same results in fixed-point theory. In this paper, motivated by this mentioned work, we show that the most best proximity point results on a metric space endowed with a partial order (under the -property) can be deduced from existing fixed-point theorems in the literature. We present various model examples to illustrate this point of view.

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Global optimal approximate solutions of best proximity points

Filomat ◽

10.2298/fil2105555h ◽

2021 ◽

Vol 35 (5) ◽

pp. 1555-1564

Author(s):

Mohammad Haddadi ◽

Vahid Parvaneh ◽

Mohammad Mursaleen

Keyword(s):

Fixed Point Theory ◽

Best Proximity Point ◽

Sufficient Conditions ◽

Approximate Solutions ◽

Point Theory ◽

Cyclic Contraction ◽

Best Proximity Points ◽

Asymptotic Contraction ◽

Global Optimal ◽

Necessary And Sufficient

In this paper, we introduce the concept of contractive pair maps and give some necessary and sufficient conditions for existence and uniqueness of best proximity points for such pairs. In our approach, some conditions have been weakened. An application has been presented to demonstrate the usability of our results. Also, we introduce the concept of cyclic ?-contraction and cyclic asymptotic ?-contraction and give some existence and convergence theorems on best proximity point for cyclic ?-contraction and cyclic asymptotic ?-contraction mappings. The presented results extend, generalize and improve some known results from best proximity point theory and fixed-point theory.

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Best Proximity Point Results inG-Metric Spaces

Abstract and Applied Analysis ◽

10.1155/2014/837943 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8 ◽

Cited By ~ 3

Author(s):

N. Hussain ◽

A. Latif ◽

P. Salimi

Keyword(s):

Fixed Point ◽

Metric Spaces ◽

Fixed Point Theory ◽

Best Proximity Point ◽

Point Theory ◽

Rich Source ◽

Point Problem ◽

Proximal Contraction ◽

Contraction Mappings

G-metric spaces proved to be a rich source for fixed point theory; however, the best proximity point problem has not been considered in such spaces. The aim of this paper is to introduce certain new classes of proximal contraction mappings and establish the best proximity point theorems for such kind of mappings inG-metric spaces. As a consequence of these results, we deduce certain new best proximity and fixed point results. Moreover, we present an example to illustrate the usability of the obtained results.

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Modeling the dynamics of hepatitis E via the Caputo–Fabrizio derivative

Mathematical Modelling of Natural Phenomena ◽

10.1051/mmnp/2018074 ◽

2019 ◽

Vol 14 (3) ◽

pp. 311 ◽

Cited By ~ 39

Author(s):

Muhammad Altaf Khan ◽

Zakia Hammouch ◽

Dumitru Baleanu

Keyword(s):

Fixed Point ◽

Existence And Uniqueness ◽

Numerical Scheme ◽

Arbitrary Order ◽

Fixed Point Theory ◽

Hepatitis E ◽

Point Theory ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Essential Properties

A virus that causes hepatitis E is known as (HEV) and regarded on of the reason for lever inflammation. In mathematical aspects a very low attention has been paid to HEV dynamics. Therefore, the present work explores the HEV dynamics in fractional derivative. The Caputo–Fabriizo derivative is used to study the dynamics of HEV. First, the essential properties of the model will be presented and then describe the HEV model with CF derivative. Application of fixed point theory is used to obtain the existence and uniqueness results associated to the model. By using Adams–Bashfirth numerical scheme the solution is obtained. Some numerical results and tables for arbitrary order derivative are presented.

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