Remarks on fixed point assertions in digital topology, 4

Laurence Boxer

Abstract

We continue the work of [4, 2, 3], in which we discuss published assertions that are incorrect or incorrectly proven; that are severely limited or reduce to triviality; or that we improve upon.

Keywords

digital topology; fixed point; metric space

Subject classification

54H25

Full Text:

PDF

References

L. Boxer, A classical construction for the digital fundamental group, Journal of Mathematical Imaging and Vision 10 (1999), 51-62. https://doi.org/10.1023/A:1008370600456

L. Boxer, Remarks on fixed point assertions in digital topology, 2, Applied General Topology 20, no. 1 (2019), 155-175. https://doi.org/10.4995/agt.2019.10667

L. Boxer, Remarks on fixed point assertions in digital topology, 3, Applied General Topology 20, no. 2 (2019), 349-361. https://doi.org/10.4995/agt.2019.11117

L. Boxer and P. C. Staecker, Remarks on fixed point assertions in digital topology, Applied General Topology 20, no. 1 (2019), 135-153. https://doi.org/10.4995/agt.2019.10474

S. Dalal, Common fixed point results for weakly compatible map in digital metric spaces, Scholars Journal of Physics, Mathematics and Statistics 4, no. 4 (2017), 196-201.

S. Dalal, I. A. Masmali, and G. Y. Alhamzi, Common fixed point results for compatible map in digital metric space, Advances in Pure Mathematics 8 (2018), 362-371. https://doi.org/10.4236/apm.2018.83019

O. Ege, D. Jain, S. Kumar, C. Park and D. Y. Shin, Commuting and compatible mappings in digital metric spaces, Journal of Fixed Point Theory and Applications 22, no. 5 (2020). https://doi.org/10.1007/s11784-019-0744-5

O. Ege and I. Karaca, Digital homotopy fixed point theory, Comptes Rendus Mathematique 353, no. 11 (2015), 1029-1033. https://doi.org/10.1016/j.crma.2015.07.006

S.-E. Han, Banach fixed point theorem from the viewpoint of digital topology, Journal of Nonlinear Science and Applications 9 (2016), 895-905. https://doi.org/10.22436/jnsa.009.03.19

K. Jyoti and A. Rani, Fixed point theorems for $beta$ - $psi$ - $phi$-expansive type mappings in digital metric spaces, Asian Journal of Mathematics and Computer Research 24, no. 2 (2018), 56-66.

K. Jyoti, A. Rani, and A. Rani, Common fixed point theorems for compatible and weakly compatible maps satisfying E.A. and CLR($T$) property in digital metric space, IJAMAA 13, no. 1 (2017), 117-128. https://doi.org/10.9734/JAMCS/2017/34278

H. K. Pathak and M. S. Khan, Compatible mappings of type (B) and common fixed point theorems of Gregus type, Czechoslovak Math. J. 45 (1995), 685-698. https://doi.org/10.21136/CMJ.1995.128555

A. Rani, K. Jyoti, and A. Rani, Common fixed point theorems in digital metric spaces, International Journal of Scientific & Engineering Research 7, no. 12 (2016), 1704-1716.

A. Rosenfeld, 'Continuous' functions on digital pictures, Pattern Recognition Letters 4 (1986), 177-184. 1986. https://doi.org/10.1016/0167-8655(86)90017-6

Abstract Views

415
Metrics Loading ...

Metrics powered by PLOS ALM


 

Cited-By (articles included in Crossref)

This journal is a Crossref Cited-by Linking member. This list shows the references that citing the article automatically, if there are. For more information about the system please visit Crossref site

1. Convexity and freezing sets in digital topology
Laurence Boxer
Applied General Topology  vol: 22  issue: 1  first page: 121  year: 2021  
doi: 10.4995/agt.2021.14185



Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt