Koreksi pada artikel Hayati dkk.: Teori Titik Tetap untuk Tipe Kannan yang Diperumum dalam Ruang b-Metrik Modular Lengkap

Afifah Hayati, Noor Sofiyati

Abstract


This article is a commentary on research that is conducted by Hayati et al. which was published in Jambura Journal of Mathematics volume 5 number 2 in 2023. It was found that there is an error occurred in the process of proving the fixed point theorems for generalized Kannan type mappings in modular b-metric spaces. This error makes the existence of the fixed point in the theorem is not valid. By adding the convex property to the modular b-metric, the fixed point theorems still holds.

Keywords


Modular b-Metric Spaces; Altering Distance Function; Kannan Type Mappings

Full Text:

PDF

References


S. Banach, “Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales,” Fundamenta mathematicae, vol. 3, no. 1, pp. 133–181, 1922. [Online]. Available: http://eudml.org/doc/213289.

R. P. Agarwal, M. Mehan, and D. O’Regan, Fixed Point Theory and Applications. Cambridge: Cambridge University Press, 2001.

R. Kannan, “Some Results on Fixed Points-II,” The American Mathematical Monthly, vol. 76, no. 4, pp. 405–408, 1969. [Online]. Available: http://www.jstor.org/stable/2316437.

J. Górnicki, “Fixed point theorems for Kannan type mappings,” Journal of Fixed Point Theory and Applications, vol. 19, pp. 2145–2152, 2017, doi: 10.1007/s11784-017-0402-8.

S. Czerwik, “Contraction Mappings in b-metric Spaces,” Acta Mathematica et Informatica Universitatis Ostraviensis, vol. 1, no. 1, pp. 5–11, 1993.[Online]. Available: https://dml.cz/handle/10338.dmlcz/120469.

V. V. Chistyakov, “Modular metric spaces, I: Basic concepts,” Nonlinier Analysis, vol. 72, pp. 1–14, 2010, doi: 10.1016/j.na.2009.04.057.

M.E. Ege and C. Alaca, “Some Results for Modular b-Metric Spaces and an Application to System of Linear Equations,” Azerbaijan Journal of Mathematics, vol. 8, no. 1, pp. 3–14, 2018. [Online]. Available: https://azjm.org/volumes/0801/0801-1.pdf.

N. Haokip and N. Goswami, “Some fixed point theorems for generalized Kannan type mappings in b-metric spaces,” Proyeccioness, Journal of Mathematics, vol. 38, no. 4, pp. 763–782, 2019, doi: 10.22199/issn.0717-6279-2019-04-0050.

A. Hayati, L. Harini, A. Winarni, and N. Muhassanah, “Teori Titik Tetap untuk Pemetaan (ψ, φ)Ω-Kontraksi pada Ruang p-Metrik Modular Berorder,” Pythagoras: Jurnal Matematika dan Pendidikan Matematika, vol. 17, no. 2, 2022, doi: 10.21831/pythagoras.v17i2.52985.

L. Harini, “Teorema Titik Tetap untuk Pemetaan Kannan Pada Ruang Metrik Modular Teritlak,” Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP), vol. 11, no. 2, pp. 11–18, 2019, doi: 10.20884/1.jmp.2019.11.2.2269.

L. Harini, H. P. Lestari, and Caturiyati, “Some fixed point theorems in generalized modular metric space,” in AIP Conference Proceedings, American Institute of Physics Inc., 2022. doi: 10.1063/5.0107775.

M. Oztürk, F. Golkarmanesh, A. Büyükkaya, and V. Parvaneh, “Generalized Almost Simulative ZˆΘΨ∗−Contraction Mappings in Modular b−Metric Spaces,” Journal of Mathematical Extension, vol. 17, no. 2, pp. 1–37, 2024, doi: 10.30495/JME.2023.2424.

P. Tyagi, S. S. Chauhan, N. Mani, and R. Shukla, “F−Modular b−Metric Spaces and Some Analogies of Classical Fixed Point Theorems,” International Journal of Analysis and Applications, vol. 22, 2024, doi: 10.28924/2291-8639-22-2024-66.

A. Hayati, N. Sofiyati, and D. L. Kartika, “Teori Titik Tetap untuk Tipe Kannan yang Diperumum dalam Ruang b-Metrik Modular Lengkap,” Jambura Journal of Mathematics, vol. 5, no. 2, 2023, doi: 10.34312/jjom.v5i2.20571.

A. Büyükkaya and M. Öztürk, “Some Common Fixed Point Results for ZE−Contractions in Modular b−Metric Spaces,” Topological Algebra and its Applications, vol. 10, no. 1, pp. 195–2015, 2022, doi: 10.1515/taa-2022-0127.

M. S. Khan, M. Swaleh, and S. Sessa, “Fixed point theorems by altering distances between the points,” Bull Aust Math Soc, vol. 30, pp. 1–9, 1984, doi: 10.1017/S0004972700001659.

H. Faraji and K. Nourouzi, “A Generalization of Kannan and Chatterjea Fixed Point Theorems on Complete b-Metric Spaces,” Sahand Communications in Mathematical Analysis, vol. 6, no. 1, pp. 77–86, 2017, doi: 10.22130/scma.2017.23831.

P. Corazza, “Introduction to Metric-Preserving Functions,” The American Mathematical Monthly, vol. 106, no. 4, pp. 309–323, 1999, doi: 10.2307/2589554.




DOI: https://doi.org/10.37905/jjom.v6i2.26441



Copyright (c) 2024 Afifah Hayati, Noor Sofiyati

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.


Jambura Journal of Mathematics has been indexed by

>>>More Indexing<<<


Creative Commons License

Jambura Journal of Mathematics (e-ISSN: 2656-1344) by Department of Mathematics Universitas Negeri Gorontalo is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. Powered by Public Knowledge Project OJS. 


Editorial Office


Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Negeri Gorontalo
Jl. Prof. Dr. Ing. B. J. Habibie, Moutong, Tilongkabila, Kabupaten Bone Bolango, Gorontalo, Indonesia
Email: info.jjom@ung.ac.id.


 

slot online slot gacor slot