Volume 19, Issue 2 (9-2024)                   IJMSI 2024, 19(2): 61-75 | Back to browse issues page

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Abdulkerim F, Koyas K, Gebregiorgis S. Coupled Coincidence and Coupled Common Fixed Points of (ψ, ϕ) Contraction Type T-coupling in Metric Spaces. IJMSI 2024; 19 (2) :61-75
URL: http://ijmsi.ir/article-1-1468-en.html
Abstract:  
In this paper, we define (ψ, ϕ)-Contraction Type T-coupling, establish a theorem satisfying such contraction condition, and prove the existence and uniqueness of coupled coincidence and coupled common fixed points in metric space. Here ψ and ϕ are two altering distance functions and T is a SCC-Map for metric spaces. Our results extend and generalize several related results in the existing literature. We also provided two examples to verify our main results.
Type of Study: Research paper | Subject: Special

References
1. H. Aydi, M. Barakat, A. Felhi, H. Isik, On ϕ-contraction Type Couplings in Partial Metric Spaces, Journal of Mathematical Analysis, 8(4), (2017), 78-89.
2. S. Banach, Sur Les Op'erations Dans Les Ensembles Abstraits et Leur Application Aux Equations Int'egrales, Fund. math, 3(1), (1922), 133-181. [DOI:10.4064/fm-3-1-133-181]
3. T. G. Bhaskar, V. Lakshmikantham, Fixed Point Theorems in Partially Ordered Metric Spaces and Applications, Nonlinear Analysis: Theory, Methods and Applications, 65(7), (2006), 1379-1393. [DOI:10.1016/j.na.2005.10.017]
4. N. Bilgili, I. M. Erhan, E. Karapinar, D. Turkoglu, A Note on Coupled Fixed Point Theorems for Mixed g-monotone Mappings in Partially Ordered Metric Spaces, Fixed Point Theory Appl., 2014(120), (2014), 6. [DOI:10.1186/1687-1812-2014-120]
5. B. S. Choudhury, A. A. Kundu, Coupled Coincidence Point Result in Partially Ordered Metric Spaces for Compatible Mappings, Nonlinear Anal., 73, (2010), 2524-2531. [DOI:10.1016/j.na.2010.06.025]
6. B. S. Choudhury, A. A. Kundu, Two Coupled Weak Contraction Theorems in Partially Ordered Metric Spaces, Revista de la Real Academia de Ciencias Exactas., Fisicas y Naturales. Serie A. Matematicas, 108, (2014), 335-351. [DOI:10.1007/s13398-012-0095-1]
7. B. S. Choudhury, P. Maity, Coupled Fixed Point Results in Generalized Metric Spaces, Math. Comput. Modelling., 54, (2011), 73-79. [DOI:10.1016/j.mcm.2011.01.036]
8. B. S. Choudhury, P. Maity, Cyclic Coupled Fixed Point Result Using Kannan Type Contractions, Journal of Operators, 108, (2014), 335-351. [DOI:10.1155/2014/876749]
9. B. S. Choudhury, P. Maity, P. Konar, Fixed Point Results for Couplings on Metric Spaces, U.P. Sci. Bull., 79, (2017), 1-12.
10. F. Gu, W. Shatanawi, Some New Results on Common Coupled Fixed Points of Two Hybrid Pairs of Mappings in Partial Metric Spaces, J. Nonlinear Funct. Anal., 2019 (2019), Article ID 13. [DOI:10.23952/jnfa.2019.13]
11. E. Karapinar, B. Alqahtani, A. Fulga, On Ciric Type −ψ− Geraghty Contractions, Thai Journal of Mathematics, 17(1), (2019), 205-216.
12. M. S. Khan, M. Swaleh, S. Sessa, Fixed Point Theorems by Altering Distances Between the Points, Bull. Aust. Math. Soc., 30, (1984), 1-9. [DOI:10.1017/S0004972700001659]
13. W. A. Kirk, P. S. Srinivasan, P. Veeramani, Fixed Points for Mappings Satisfying Cyclical Contractive Conditions, Fixed Point Theory, 4, (2003), 78-89.
14. V. Lakshmikantham, L. Ciric, Coupled Fixed Point Theorems for Nonlinear Contractions in Partially Ordered Metric Spaces, Nonlinear Anal., 70, (2009), 4341-4349. [DOI:10.1016/j.na.2008.09.020]
15. V. I. Opoitsev, Dynamics of Collective Behavior-Heterogenic Systems, Avtom. Telemeh., 36, (1975a), 124-138.
16. V. I. Opoitsev, Heterogenic and Combined-concave Operators, Sib. Math. J., 16, (1975b), 781-792. [DOI:10.1007/BF00967133]
17. V. I. Opoitsev, T. A. Khurodze, Nonlinear Operators in Spaces with a Cone, Tbilis. Gos. Univ., (1984), 271.
18. A. Petrusel, G. Petrusel, Fixed Point Results for Multi-valued Locally Contractive Operators, Appl. Set-Valued Anal. Optim., 2(2), (2020), 175-181. [DOI:10.23952/asvao.2.2020.2.04]
19. K. P. R. Rao, Coupled Coincidence Point Theorems for (ψ, α, β)-Weak Contractions in Partially Ordered Partial Metric Spaces, Punjab University Journal of Mathematics, 45, (2013), 51-62.
20. T. Rashid, Q. H. Khan, Coupled Coincidence Point of ϕ-Contraction Type TCoupling and (ψ, ϕ)-Contraction Type Coupling in Metric Spaces, arXiv preprint arXiv:1710.10054 (2017).
21. B. Samet, C. Vetro, Coupled Fixed Point Theorems for Multi-valued Nonlinear Contraction Mappings in Partially Ordered Metric Spaces, Nonlinear Analysis: Theory, Methods & Applications, 74(12), (2011), 4260-4268. [DOI:10.1016/j.na.2011.04.007]
22. M. Simkhah, D. Turkoglu, S. Sedghi, N. Shobe, Suzuki Type Fixed Point Results in p-metric Spaces, Commun. Optim. Theory, 2019(2019), Article ID 13.
23. N. Van Luong, N. X. Thuan, Coupled Fixed Points in Partially Ordered Metric Spaces and Application, Nonlinear Analysis: Theory, Methods & Applications, 74(3), (2011), 983-992. [DOI:10.1016/j.na.2010.09.055]

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