Zamfirescu mappings under Pata-type condition: results and application to an integral equation
Abstract
Introduction/purpose: Pata-type and Zamfirescu mappings are extended beyond metric spaces.
Methods: The concept of Pata-type Zamfirescu mapping within the framework of S-metric spaces is employed.
Results: A series of corresponding outcomes has been established. Furthermore, the obtained results are employed to solve an integral equation.
Conclusions: S-Pata type and Zamfirescu mappings have unique fixed points.
References
Aktay, M. & Özdemir, M. 2022. On (α, φ)-weak Pata contractions. MANAS Journal of Engineering, 10(2), pp. 228–240. Available at: https://doi.org/10.51354/mjen.1085695.
Alghamdi, M.A., Gulyaz-Ozyurt, S. & Fulga, A. 2021. Fixed points of Proinov E−contractions. Symmetry, 13(6), art.number:962. Available at: https://doi.org/10.3390/sym13060962.
Banach, S. 1922. Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fundamenta mathematicae, 3, pp. 133–181. Available at: https://doi.org/10.4064/fm-3-1-133-181.
Chand, D. & Rohen, Y. 2023. Fixed Points of (αs−βs−ψ)-Contractive Mappings in S-Metric Spaces. Nonlinear Functional Analysis and Applications, 28(2), pp. 571–587. Available at: https://doi.org/10.22771/nfaa.2023.28.02.15.
Chatterjea, S. 1972. Fixed-point theorems. Dokladi na Bolgarskata Akademiya na Naukite, 25(6), p. 727.
Jacob, G.K., Khan, M.S., Park, C. & Yun, S. 2018. On Generalized Pata Type Contractions. Mathematics, 6(2), art.number:25. Available at: https://doi.org/10.3390/math6020025.
Kadelburg, Z. & Radenović, S. 2014. Fixed Point and Tripled Fixed Point Theorems under Pata-Type Conditions in Ordered Metric Spaces. International Journal of Analysis and Applications, 6(1), pp. 113–122 [online]. Available at: https://www.etamaths.com/index.php/ijaa/article/view/392 [Accessed: 7 February 2024].
Kadelburg, Z. & Radenović, S. 2016. Fixed point theorems under Pata-type conditions in metric spaces. Journal of the Egyptian Mathematical Society, 24(1), pp. 77–82. Available at: https://doi.org/10.1016/j.joems.2014.09.001.
Kannan, R. 1968. Some results on fixed points. Bulletin of the Calcutta Mathematical Society, 60, pp. 71–76.
Karapinar, E., Fulga, A. & Aydi, H. 2020a. Study on Pata E−contractions. Advances in Difference Equations, 2020, art.number:539. Available at: https://doi.org/10.1186/s13662-020-02992-4.
Karapınar, E., Fulga, A. & Rakočević, V. 2020b. A discussion on a Pata type contraction via iterate at a point. Filomat, 34(4), pp. 1061–1066. Available at: https://doi.org/10.2298/FIL2004061K.
Özgür, N. & Taş, N. 2021. Pata Zamfirescu Type Fixed-Disc Results with a Proximal Application. Bulletin of the Malaysian Mathematical Sciences Society, 44, pp. 2049–2061. Available at: https://doi.org/10.1007/s40840-020-01048-w.
Özgür, N. & Taş, N. 2023. On S-metric spaces with some topological aspects. Electronic Journal of Mathematical Analysis and Applications, 11(2), pp. 1–8. Available at: https://doi.org/10.21608/ejmaa.2023.206319.1029.
Pata, V. 2011. A fixed point theorem in metric spaces. Journal of Fixed Point Theory and Applications, 10(2), pp. 299–305. Available at: https://doi.org/10.1007/s11784-011-0060-1.
Priyobarta, N., Rohen, Y., Thounaojam, S. & Radenović, S. 2022. Some remarks on α-admissibility in S−metric spaces. Journal of Inequalities and Applications, 2022, art.number:34. Available at: https://doi.org/10.1186/s13660-022-02767-3.
Roy, S., Chakraborty, P., Ghosh, S., Saha, P. & Choudhury, B.S. 2024. Investigation of a fixed point problem for Pata-type contractions with respect to w-distance. The Journal of Analysis, 32, pp. 125–136. Available at: https://doi.org/10.1007/s41478-023-00612-4.
Saleem, N., Abbas, M., Bin-Mohsin, B. & Radenovic, S. 2020. Pata type best proximity point results in metric spaces. Miskolc Mathematical Notes, 21(1), pp. 367–386. Available at: https://doi.org/10.18514/MMN.2020.2764.
Sedghi, S., Shobe, N. & Aliouche, A. 2012. A generalization of fixed point theorems in S-metric spaces. Matematički vesnik, 64(3), pp. 258–266 [online]. Available at: http://www.vesnik.math.rs/landing.php?p=mv123.cap&name=mv12 309 [Accessed: 7 February 2024].
Yahaya, S., Shagari, M.S. & Ali, T.A. 2023. Multivalued hybrid contraction that involves Jaggi and Pata-type inequalities. Mathematical Foundations of Computing. Available at: https://doi.org/10.3934/mfc.2023045.
Zamfirescu, T. 1972. Fix point theorems in metric spaces. Archiv der Mathematik, 23. Available at: https://doi.org/10.1007/BF01304884.
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