Partial Order, Fixed Point Theory, Variational Principles

We presented some maximal and minimal fixed point theorems of set-valued monotone mappings with respect to a partial order introduced by a vector functional in cone metric spaces. In addition, we proved not only the existence of maximal and minimal fixed points but also the existence of the largest and the least fixed points of single-valued increasing mappings. It is worth mentioning that the results on single-valued mappings in this paper are still new even in the case of metric spaces and hence they indeed improve the recent results.

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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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Maximality, fixed points and variational principles for mappings on quasi-uniform spaces

Filomat ◽

10.2298/fil1716345f ◽

2017 ◽

Vol 31 (16) ◽

pp. 5345-5355

Author(s):

Raúl Fierro

Keyword(s):

Fixed Point ◽

Fixed Points ◽

Metric Spaces ◽

Variational Principles ◽

Fixed Point Theory ◽

Point Theory ◽

Uniform Structure ◽

Uniform Spaces ◽

Order Relations ◽

And Variational Principles

By making use of maximality on some appropriate preorderings, some classical results stated in the context of metric spaces are extended to spaces endowed with quasi-uniform structures. Indeed, various results on fixed point theory and variational principles have been proved by arguments using order relations in metric spaces. In this work, some of the mentioned results are extended to spaces having a quasi-uniform structure, by means of appropriate preorderings. The concept of w-distance is used to this purpose. Moreover, equivalences of maximality are stated for general preorderings.

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From graphical metric spaces to fixed point theory in binary related distance spaces

Filomat ◽

10.2298/fil1711209r ◽

2017 ◽

Vol 31 (11) ◽

pp. 3209-3231 ◽

Cited By ~ 4

Author(s):

López Roldán ◽

Naseer Shahzad

Keyword(s):

Fixed Point ◽

Partial Order ◽

Binary Relation ◽

Directed Graph ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Fixed Point Theory ◽

Point Theory ◽

Transitive Relation ◽

Ordered Metric Spaces

Very recently, many fixed point results have been introduced in the setting of graphical metric spaces. Due to their intimate links, such works also deal with metric spaces endowed with partial orders. As the reachability relationship in any directed graph (containing all cycles) is a reflexive transitive relation (that is, a preorder), but it is not necessarily a partial order, results on graphical metric spaces are independent from statements on ordered metric spaces. The main aim of this paper is to show that fixed point theorems in the setting of graphical metric spaces can be directly deduced from their corresponding results on measurable spaces endowed with a binary relation. Finally, we also describe the main advantages of involving this last class of spaces.

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On a pair of fuzzy mappings in modular-like metric spaces with applications

Advances in Difference Equations ◽

10.1186/s13662-021-03398-6 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Tahair Rasham ◽

Abdullah Shoaib ◽

Choonkill Park ◽

Ravi P. Agarwal ◽

Hassen Aydi

Keyword(s):

Fixed Point ◽

Partial Order ◽

Integral Equations ◽

Metric Spaces ◽

Fixed Point Theory ◽

Point Theory ◽

Volterra Type ◽

Existence Of A Solution ◽

Type Integral

AbstractThe aim of this work is to establish results in fixed point theory for a pair of fuzzy dominated mappings which forms a rational fuzzy dominated V-contraction in modular-like metric spaces. Some results via a partial order and using the graph concept are also developed. We apply our results to ensure the existence of a solution of nonlinear Volterra-type integral equations.

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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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