Remarks on fixed point assertions in digital topology, 5

Laurence Boxer

doi:10.4995/agt.2022.16655

Authors

Laurence Boxer Niagara University https://orcid.org/0000-0001-7905-9643

DOI:

https://doi.org/10.4995/agt.2022.16655

Keywords:

digital topology, fixed point, metric space

Abstract

As in [6, 3, 4, 5], we discuss published assertions concerning fixed points in “digital metric spaces” - assertions that are incorrect or incorrectly proven, or reduce to triviality.

Downloads

Download data is not yet available.

Author Biography

Laurence Boxer, Niagara University

Department of Computer and Information Sciences ; Department of Computer Science and Engineering, State University of New York at Buffalo

References

S. K. Barve, Q. A. Kabir and R. D. Daheriya, Unique common fixed point theorem for weakly compatible mappings in digital metric space, International Journal of Scientific Research and Reviews 8, no. 1 (2019), 2114-2121.

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, Remarks on fixed point assertions in digital topology, 4, Applied General Topology 21, no. 2 (2020), 265-284. https://doi.org/10.4995/agt.2020.13075

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

C. Chauhan, J. Singhal, S. Shrivastava, Q. A. Kabir and P. K. Jha, Digital topology with fixed point, Materials Today: Proceedings 47 (2021), 7167-7169. https://doi.org/10.1016/j.matpr.2021.06.358

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.

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

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.

K. Jyoti and A. Rani, Fixed point theorems with digital contractions, International Journal of Current Advanced Research 7, no. 3(E) (2018), 10768-10772.

A. Mishra, P. K. Tripathi, A. K. Agrawal and D. R. Joshi, A contraction mapping method in digital image processing, International Journal of Recent Technology and Engineering 8, no. 4S5 (2019), 193-196. https://doi.org/10.35940/ijrte.D1046.1284S519

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.

K. Rana and A. Garg, Various contraction conditions in digital metric spaces, Advances in Mathematics: Scientific Journal 9, no. 8 (2020), 5433-5441. https://doi.org/10.37418/amsj.9.8.14

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