Remarks on fixed point assertions in digital topology, 2

Authors

  • Laurence Boxer Niagara University

DOI:

https://doi.org/10.4995/agt.2019.10667

Keywords:

digital topology, fixed point, metric space

Abstract

Several recent papers in digital topology have sought to obtain fixed point results by mimicking the use of tools from classical topology, such as complete metric spaces. We show that in many cases, researchers using these tools have derived conclusions that are incorrect, trivial, or limited.

Downloads

Download data is not yet available.

Author Biography

Laurence Boxer, Niagara University

Department of Computer and Information Sciences

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, Generalized normal product adjacency in digital topology, Applied General Topology 18, no. 2 (2017), 401-427. https://doi.org/10.4995/agt.2017.7798

L. Boxer, Alternate product adjacencies in digital topology, Applied General Topology 19, no. 1 (2018), 21-53. https://doi.org/10.4995/agt.2018.7146

L. Boxer, O. Ege, I. Karaca, J. Lopez and J. Louwsma, Digital fixed points, approximate fixed points, and universal functions, Applied General Topology 17, no. 2 (2016), 159-172. https://doi.org/10.4995/agt.2016.4704

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

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

U. P. Dolhare and V. V. Nalawade, Fixed point theorems in digital images and applications to fractal image compression, Asian Journal of Mathematics and Computer Research 25, no. 1 (2018), 18-37.

O. Ege and I. Karaca, Banach fixed point theorem for digital images, Journal of Nonlinear Sciences and Applications 8 (2015), 237-245. https://doi.org/10.22436/jnsa.008.03.08

G. Herman, Oriented surfaces in digital spaces, CVGIP: Graphical Models and Image Processing 55 (1993), 381-396. https://doi.org/10.1006/cgip.1993.1029

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

A. Hossain, R. Ferdausi, S. Mondal and H. Rashid, Banach and Edelstein fixed point theorems for digital images, Journal of Mathematical Sciences and Applications 5, no. 2 (2017), 36-39. https://doi.org/10.12691/jmsa-5-2-2

D. Jain, Common fixed point theorem for intimate mappings in digital metric spaces, International Journal of Mathematics Trends and Technology 56, no. 2 (2018), 91-94. https://doi.org/10.14445/22315373/IJMTT-V56P511

K. Jyoti and A. Rani, Fixed point results for expansive mappings in digital metric spaces, International Journal of Mathematical Archive 8, no. 6 (2017), 265-270.

K. Jyoti and A. Rani, Digital expansions endowed with fixed point theory, Turkish Journal of Analysis and Number Theory 5, no. 5 (2017), 146-152. https://doi.org/10.12691/tjant-5-5-1

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

L. N. Mishra, K. Jyoti, A. Rani and Vandana, Fixed point theorems with digital contractions image processing, Nonlinear Science Letters A 9, no. 2 (2018), 104-115.

C. Park, O. Ege, S. Kumar, D. Jain and J. R. Lee, Fixed point theorems for various contraction conditions in digital metric spaces, Journal of Computational Analysis and Applications 26, no. 8 (2019), 1451-1458.

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), 1704-1715.

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

B. Samet, C. Vetro, and P. Vetro, Fixed point theorems for contractive mappings, Nonlinear Analysis: Theory, Methods & Applications 75, no. 4 (2012), 2154-2165. https://doi.org/10.1016/j.na.2011.10.014

K. Sridevi, M. V. R. Kameswari and D. M. K. Kiran, Fixed point theorems for digital contractive type mappings in digital metric spaces, International Journal of Mathematics Trends and Technology 48, no. 3 (2017), 159-167. https://doi.org/10.14445/22315373/IJMTT-V48P522

K. Sridevi, M. V. R. Kameswari and D. M. K. Kiran, Common fixed points for commuting and weakly compatible self-maps on digital metric spaces, International Advanced Research Journal in Science, Engineering and Technology 4, no. 9 (2017), 21-27.

Downloads

Published

2019-04-01

How to Cite

[1]
L. Boxer, “Remarks on fixed point assertions in digital topology, 2”, Appl. Gen. Topol., vol. 20, no. 1, pp. 155–175, Apr. 2019.

Issue

Section

Articles