Teorema Titik Tetap untuk Pemetaan Kannan dan Chatterjea pada Ruang Metrik Modular Bernilai Kompleks
Abstract
In this paper, inspired by fixed point concepts of complex valued modular metric space, we introduce Kannan complex and Chatterjea complex mappings. Using this new idea, some fixed point theorems involving both of these contractive mappings are established. Furthermore, existence and uniqueness of fixed point for Kannan complex and Chatterjea complex mappings on complex valued modular metric space is proved.
References
Abdou, A. A., & Khamsi, M. A. (2013). Fixed point results of pointwise contractions in modular metric spaces. Fixed Point Theory and Applications, 2013, 1-11. https://doi.org/10.1186/1687-1812-2013-163
Aksoy, Ü., Karapınar, E., & Erhan, İ. M. (2017). Fixed point theorems in complete modular metric spaces and an application to anti-periodic boundary value problems. Filomat, 31(17), 5475-5488. https://doi.org/10.2298/fil1717475a
Azam, A., Fisher, B., & Khan, M. (2011). Common fixed point theorems in complex valued metric spaces. Numerical Functional Analysis and Optimization, 32(3), 243-253.
Chistyakov, V. V. (2006, January). Metric modulars and their application. In Doklady Mathematics (Vol. 73, pp. 32-35). Nauka/Interperiodica. https://doi.org/10.1134/S106456240601008X
Chistyakov VV. (2011). A fixed point theorem for contractions in modular metric spaces. e-Print, arXiv:1112.5561. 1–31. https://doi.org/10.48550/arXiv.1112.5561
Ege, M. E., & Alaca, C. (2015). Fixed point results and an application to homotopy in modular metric spaces. Journal of Nonlinear Sciences and Applications, 8(6), 900-908. https://doi.org/10.22436/jnsa.008.06.01
Mongkolkeha, C., Sintunavarat, W., & Kumam, P. (2011). Fixed point theorems for contraction mappings in modular metric spaces. Fixed Point Theory and Applications, 2011(1), 1-9. https://doi.org/10.1186/1687-1812-2011-93
Özkan, K., Gürdal, U., & Mutlu, A. (2021). Some fixed point theorems on complex valued modular metric spaces with an application. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70(2), 690-701. https://doi.org/10.31801/cfsuasmas.727771
Sitthikul, K., & Saejung, S. (2012). Some fixed point theorems in complex valued metric spaces. Fixed Point Theory and Applications, 2012(1), 1-11. https://doi.org/10.1186/1687-1812-2012-189
Zhao, J., Zhao, Q., Jin, B., & Zhong, L. (2018). Fixed Point Results for Weakly C-Contraction Mapping in Modular Metric Spaces. Open Access Library Journal, 5(1), 1-9. https://doi.org/10.4236/oalib.1104061
- View 179 times Download 179 times PDF
Copyright (c) 2023 Mariatul Kiftiah, Yudhi Yudhi
This work is licensed under a Creative Commons Attribution 4.0 International License.