Remarks on fixed point assertions in digital topology, 8
Submitted: 2024-01-18
|Accepted: 2024-03-21
|Published: 2024-10-01
Copyright (c) 2024 Laurence Boxer
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Downloads
Keywords:
digital topology, digital image, fixed point, digital metric space
Supporting agencies:
Abstract:
This paper continues a series in which we study deficiencies in previously published works concerning fixed point assertions for digital images.
References:
T. Botmart, A. Shaheen, A. Batool, S. Etemad, and S. Rezapour, A novel scheme of k-step iterations in digital metric spaces, AIMS Math. 8, no. 1 (2023), 873-886. https://doi.org/10.3934/math.2023042
L. Boxer, A classical construction for the digital fundamental group, J. Math. Imaging Vision 10 (1999), 51-62. https://doi.org/10.1023/A:1008370600456
L. Boxer, Remarks on fixed point assertions in digital topology, 2, Appl. Gen. Topol. 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, Appl. Gen. Topol. 20, no. 2 (2019), 349-361. https://doi.org/10.4995/agt.2019.11117
L. Boxer, Fixed point sets in digital topology, 2, Appl. Gen. Topol. 21, no. 1 (2020), 111-133. https://doi.org/10.4995/agt.2020.12101
L. Boxer, Remarks on fixed point assertions in digital topology, 4, Appl. Gen. Topol. 21, no. 2 (2020), 265-284. https://doi.org/10.4995/agt.2020.13075
L. Boxer, Remarks on fixed point assertions in digital topology, 5, Appl. Gen. Topol. 23, no. 2 (2022) 437-451. https://doi.org/10.4995/agt.2022.16655
L. Boxer, Remarks on fixed point assertions in digital topology, 6, Appl. Gen. Topol. 24, no. 2 (2023), 281-305. https://doi.org/10.4995/agt.2023.18996
L. Boxer, Remarks on fixed point assertions in digital topology, 7, Appl. Gen. Topol. 25, no. 1 (2024), 97-115. https://doi.org/10.4995/agt.2024.20026
L. Boxer and P.C. Staecker, Remarks on fixed point assertions in digital topology, Appl. Gen. Topol. 20, no. 1 (2019), 135-153. https://doi.org/10.4995/agt.2019.10474
G. Chartrand and S. Tian, Distance in digraphs, Comput. Math. Appl. 34, no. 11 (1997), 15-23. https://doi.org/10.1016/S0898-1221(97)00216-2
B. Dass and S. Gupta, An extension of Banach's contraction principle through rational expression, Indian J. Pure Appl. Math. 6 (1975), 1455-1458.
O. Ege and I. Karaca, Digital homotopy fixed point theory, C. R. Math. Acad. Sci. Paris 353, no. 11 (2015), 1029-1033. https://doi.org/10.1016/j.crma.2015.07.006
O. Ege and I. Karaca, Banach fixed point theorem for digital images, J. Nonlinear Sci. Appl. 8, no. 3 (2015), 237-245. https://doi.org/10.22436/jnsa.008.03.08
N. Gupta, A. Singh, and G. Modi, Application of fixed point theorems for digital contractive type mappings in digital metric space, Int. J. Sci. Res. in Math. Stat. Sci. 6, no. 1 (2019), 323-327.
S. E. Han, Banach fixed point theorem from the viewpoint of digital topology, J. Nonlinear Sci. Appl. 9 (2016), 895-905. https://doi.org/10.22436/jnsa.009.03.19
D. Jain, Expansive mappings in digital metric spaces, Bull. Pure Appl. Sci. 37E (Math & Stat.), no. 1 (2018), 101-108. https://doi.org/10.5958/2320-3226.2018.00011.5
K. Jyoti, A. Rani, and A. Rani, Digital-β-ψ-contractive type mappings in digital metric spaces, Int. Rev. Pure Appl. Math. 13, no. 1 (2017), 101-110. https://doi.org/10.5958/2320-3226.2018.00011.5
K. Jyoti and A. Rani, Fixed point theorems for β-ψ-ϕ-expansive type mappings in digital metric spaces, Asian J. Math. Comput. Res. 24, no. 2 (2018), 56-66.
E. Khalimsky, Motion, deformation, and homotopy in finite spaces, Proc. IEEE Intl. Conf. Systems, Man, Cybernetics (1987), 227-234.
A. Khan, Unique fixed point theorem for weakly digital metric spaces involving auxiliary functions, Int. J. of Math. Appl. 11, no. 2 (2023), 71-78.
A. Mishra, P. K. Tripathi, A. K. Agrawal, and D. R. Joshi, Common fixed point under Jungck contractive condition in a digital metric space, J. of Math. Comput. Sci. 11, no. 3 (2021), 3067-3079.
R. Pal, Application of fixed point theorem for digital images, Int. J. Adv. Res. 10, no. 1 (2022), 1110-1126. https://doi.org/10.21474/IJAR01/14152
A. Rani, K. Jyoti and A. Rani, Common fixed point theorems in digital metric spaces, Int. J. of Sci. Eng. Res. 7, no. 12 (2016), 1704-1715. https://doi.org/10.51983/ajsat-2018.7.2.1035
A. Rosenfeld, 'Continuous' functions on digital pictures, Pattern Recogn. Lett. 4 (1986), 177 - 184. https://doi.org/10.1016/0167-8655(86)90017-6
A. S. Saluja and J. Jhade, Dass and Gupta's fixed-point theorem in digital metric space, Int. J. Math. Comput. Res. 11, no. 12 (2023), 3899-3901. https://doi.org/10.47191/ijmcr/v11i12.03
B. Samet, C. Vetro, and P. Vetro, Fixed point theorems for α-ψ-contractive mappings, Nonlinear Anal.: Theory, Methods Appl. 75, no. 4 (2012), 2154-2165. https://doi.org/10.1016/j.na.2011.10.014
K. Shukla, Some fixed point theorems in digital metric spaces satisfying certain rational inequalities, J. Emerging Technol. Innovative Res. 5, no. 12 (2018), 383-389.
K. Sridevi, M. V. R. Kameshwari, and D. M. K. Kiran, Fixed point theorem for digital contractive type mappings in digital metric space, Int. J. of Math. Trends Technol. 48, no. 3 (2017), 159-167. https://doi.org/10.14445/22315373/IJMTT-V48P522
