Lefschetz fixed point theory for admissible maps on Hausdorff topological spaces

Unlike the study of the fixed point property (FPP, for brevity) of retractable topological spaces, the research of the FPP of non-retractable topological spaces remains. The present paper deals with the issue. Based on order-theoretic foundations and fixed point theory for Khalimsky (K-, for short) topological spaces, the present paper studies the product property of the FPP for K-topological spaces. Furthermore, the paper investigates the FPP of various types of connected K-topological spaces such as non-K-retractable spaces and some points deleted K-topological (finite) planes, and so on. To be specific, after proving that not every one point deleted subspace of a finite K-topological plane X is a K-retract of X, we study the FPP of a non-retractable topological space Y, such as one point deleted space Y ∖ { p } .

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Fixed point theory for extension type maps in topological spaces

Applicable Analysis ◽

10.1080/00036810802713941 ◽

2009 ◽

Vol 88 (2) ◽

pp. 301-308 ◽

Cited By ~ 2

Author(s):

Donal O'Regan

Keyword(s):

Fixed Point ◽

Fixed Point Theory ◽

Point Theory ◽

Topological Spaces

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Links between Contractibility and Fixed Point Property for Khalimsky Topological Spaces

Mathematics ◽

10.3390/math8010018 ◽

2019 ◽

Vol 8 (1) ◽

pp. 18

Author(s):

Sang-Eon Han

Keyword(s):

Fixed Point ◽

Topological Space ◽

Fixed Point Theory ◽

Point Theory ◽

Fixed Point Property ◽

Topological Spaces ◽

Point Property ◽

Continuous Maps

Given a Khalimsky (for short, K-) topological space X, the present paper examines if there are some relationships between the contractibility of X and the existence of the fixed point property of X. Based on a K-homotopy for K-topological spaces, we firstly prove that a K-homeomorphism preserves a K-homotopy between two K-continuous maps. Thus, we obtain that a K-homeomorphism preserves K-contractibility. Besides, the present paper proves that every simple closed K-curve in the n-dimensional K-topological space, S C K n , l , n ≥ 2 , l ≥ 4 , is not K-contractible. This feature plays an important role in fixed point theory for K-topological spaces. In addition, given a K-topological space X, after developing the notion of K-contractibility relative to each singleton { x } ( ⊂ X ) , we firstly compare it with the concept of K-contractibility of X. Finally, we prove that the K-contractibility does not imply the K-contractibility relative to each singleton { x 0 } ( ⊂ X ) . Furthermore, we deal with certain conjectures involving the (almost) fixed point property in the categories KTC and KAC, where KTC (see Section 3) (resp. KAC (see Section 5)) denotes the category of K-topological (resp. KA-) spaces, KA-) spaces are subgraphs of the connectedness graphs of the K-topology on Z n .

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Relative Extension of Continuous Mappings

Journal of Advances in Mathematics and Computer Science ◽

10.9734/jamcs/2020/v35i230246 ◽

2020 ◽

pp. 12-24

Author(s):

Miroslaw Slosarski

Keyword(s):

Fixed Point ◽

Fixed Point Theory ◽

Point Theory ◽

Topological Spaces ◽

Relative Extension ◽

Continuous Mappings

In this paper, the notion of a relative extension of continuous mappings is defined. The relative extension of continuous mappings is the generalization of the notion of a relative retract in topological spaces. The relative extension of continuous mappings will be applied to fixed point theory.

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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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