| Keywords and phrases: partially-order, fixed point theorem, nonlinear fractional system.
Received: September 23, 2023; Revised: October 6, 2023; Accepted: November 25, 2023
How to cite this article: Jing Ren and Chengbo Zhai, Fixed point theorems in product spaces and application to a nonlinear fractional system, JP Journal of Fixed Point Theory and Applications 20 (2024), 1-24. http://dx.doi.org/10.17654/0973422824001
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License 
References:
[1] R. P. Agarwal and D. O’Regan, Cone compression and expansion fixed point theorems in Fréchet spaces with applications, J. Differential Equations 171 (2001), 412-429.
[2] H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Rev. 18(4) (1976), 620-709.
[3] L. Cheng and C. Huang, On distal flows and common fixed point theorems in Banach spaces, J. Math. Anal. Appl. 523 (2023), Paper No. 126995, 10 pp. DOI:10.1016/j.jmaa.2022.126995.
[4] A. Fora, A fixed point theorem for product spaces, Pacific J. Math. 99(2) (1982), 327-335.
[5] D. Guo and V. Lakshmikantham, Coupled fixed points of nonlinear operators with applications, Nonlinear Anal. 11(5) (1987), 623-632.
[6] D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press Inc, Boston and New York, 1988.
[7] G. Hami, Ö. Mahpeyker and G. Ömer Faruk, Fixed point theorems of new generalized C-conditions for -mappings in modular metric spaces and its applications, Nonlinear Anal. Model. Control. 28 (2023), 949-970.
[8] J. Matkowski, A generalization of the Goebel-Kirk fixed point theorem for asymptotically nonexpansive mappings, J. Fixed Point Theory Appl. 25 (2023), 1-6.
[9] M. Kazemi and A. R. Yaghoobnia, Application of fixed point theorem to solvability of functional stochastic integral equations, Appl. Math. Comput. 417 (2022), Paper No. 126759, 11 pp.
[10] U. Kohlenbach and L. Leustean, The approximate fixed point property in product spaces, Nonlinear Anal. 66 (2007), 806-818.
[11] T. Kuczumow, Fixed point theorems in product spaces, Proc. Amer. Math. Soc. 108(3) (1990), 727-729.
[12] K. Latrach, M. A. Taoudi and A. Zeghal, Some fixed point theorems of the Schauder and the Krasnosel’skii type and application to nonlinear transport equations, J. Differential Equations 221 (2006), 256-271.
[13] J. J. Nieto, R. L. Pouso and R. Rodriguez-Lopez, Fixed point theorems in ordered abstract spaces, Proc. Amer. Math. Soc. 135 (2007), 2505-2517.
[14] R. Kumar and S. Kumar, Common fixed point theorems for faintly compatible maps satisfying weak contraction condition, Bull. Calcutta Math. Soc. 114 (2022), 897-908.
[15] K. K. Tan and H. K. Xu, On fixed point theorems of nonexpansive mappings in product spaces, Proc. Amer. Math. Soc. 113(4) (1991), 983-989.
[16] H. Tamimi, S. Saiedinezhad and M. B. Ghaemi, The measure of noncompactness in a generalized coupled fixed point theorem and its application to an integro-differential system, J. Comput. Appl. Math. 413 (2022), Paper No. 114380, 16 pp.
[17] A. Wiśnicki, On the super fixed point property in product spaces, J. Funct. Anal. 236 (2006), 447-456.
[18] C. S. Goodrich, Existence of a positive solution to systems of differential equations of fractional order, Comput. Math. Appl. 62 (2011), 1251-1268.
[19] C. B. Zhai and J. Ren, Some properties of sets, fixed point theorems in ordered product spaces and applicatio.ns to a nonlinear system of fractional differential equations, Topol. Methods Nonlinear Anal. 49 (2017), 625-645.
[20] C. B. Zhai and M. R. Hao, Fixed point theorems for mixed monotone operators with perturbation and applications to fractional differential equation boundary value problems, Nonlinear Anal. 75 (2012), 2542-2551.
[21] C. B. Zhai and L. Xu, Properties of positive solutions to a class of four-point boundary value problem of Caputo fractional differential equations with a parameter, Commun. Nonlinear Sci. Numer. Simul. 19 (2014), 2820-2827.
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