Fixed points and dynamic programming in complex valued-controlled metric spaces
DOI:
https://doi.org/10.24193/subbmath.2026.1.10Keywords:
Reich-type contraction, common fixed point, dynamic programmingAbstract
In this paper, we introduce the concepts of (α − Θ)-contraction and Reich-type contraction within the framework of complex valued-controlled metric spaces (CVCMS). We also present related fixed point theorems for CVCMS, building on the works considered in the literature review for controlled metric type spaces. To demonstrate the practical implications and significance of our results, we provide several examples and an application in dynamic programming.
References
[1] Ahmad, J., Al-Mazrooei, A.E., Aydi, H., De la Sen, M., On Fixed Point Results in Controlled Metric Spaces, J. Funct., 2020, 2108167.
[2] Ahmad, J., Lateef, D., Fixed point theorems for rational type (α − Θ)-contractions in controlled metric spaces, J. Nonlinear Sci. Appl., 13(2020), 163–170.
[3] Al-Mazrooei, A.E., Ahmad, J., Fixed Point Results in Controlled Metric Spaces with Applications, Mathematics, 10(3)(2022), 490 pp. https://doi.org/10.3390/math10030490
[4] Arutyunov, A., Jaćimović, V., Pereira, F., Second order necessary conditions for optimal impulsive control problems, Journal of Dynamical and Control Systems, 9(1)(2022), 131153.
[5] Aslam, M.S., Chowdhury, M.S.R., Guran, L., Alqudah, M. A., Abdeljawad, T. Fixed point theory in complex valued controlled metric spaces with an application, AIMS Mathematics, 7(7)(2022), 11879-11904.
[6] Azam, A., Ahmad, J., Kumam, P., Common fixed point theorems for multi-valued mappings in complex valued metric spaces, Journal of Inequalities and Applications, 1(2013), 578 pp.
[7] Banach, S., Sur les operation dans les ensembles abstraits et applications aux equations integrals, Fund. Math., 1922, 133-181.
[8] Belhenniche A., Benahmed S., Pereira F.L., Extension of λ-PIR for weakly contractive operators via fixed point theory, Fixed Point Theory, 22(2)(2021), 511-526. doi:10.24193/fpt-ro.2021.2.34.
[9] Belhenniche, A., Benahmed, S., Guran, L., Existence of a solution for integral Urysohn type equations system via fixed points technique in complex valued extended b-metric spaces, Journal of Prime Research in Mathematics, 16(2)(2020), 109-122.
[10] Bellman, R. The theory of dynamic programming, Rand Corporation Report Santa Monica, CA, 1954, 550 pp.
[11] Bertsekas, D.P., Dynamic Programming and Optimal Control, Athena Scientific, 2005.
[12] Bertsekas, D.P., Ioffe, S., Temporal differences-based policy iteration and applications in neuro-dynamic programming, Lab. for Info. and Decision Systems Report, 1996, 2349.
[13] Bertsekas, D.P., Tsitsiklis, J.N., Neuro-dynamic programming, Athena Scientific, 1996.
[14] Fraga, S., Pereira, F., Hamilton-Jacobi-Bellman equation and feedback synthesis for impulsive control, IEEE Transactions on Automatic Control, 57(1)(2021), 244-249.
[15] Hussain, S., Fixed Point Theorems For Nonlinear Contraction In Controlled Metric Type Space, Applied Mathematics E-Notes, 21(2021), 53-61.
[16] Karamzin, D., De Oliveira, V., Pereira, F., Silva, G., On some extension of optimal control theory, European Journal of Control, 20(6)(2014), 284-291.
[17] Lateef, D., Fisher type fixed point results in controlled metric spaces,Journal of Mathematics and Computer Science, 20(2020), 234-240.
[18] Lateef, D., Kannan fixed point theorem in C-metric spaces, Journal of Mathematical Analysis, 10(5)(2019), 34-40.
[19] Mlaiki, N., Aydi, H., Souayah, N., Abdeljawad, T. Controlled metric type spaces and related contraction principle, Mathematics, 6(10)(2018), 1-6.
[20] Mlaiki, N., Aydi, H., Souayah, N., Abdeljawad, T. An Improvement of Recent Results in Controlled Metric Type Spaces, Filomat, 34(6)(2020), 1853–1862.
[21] Panday, B., Pandey, A. K., Ughade, M., Rational Type Contraction In Controlled Metric Spaces, J. Math. Comput. Sci., 11(4)(2021), 4631-4639.
[22] Rao, K. P.R., Swamy, P.R., Prasad, J.R., A common fixed point theorem in complex valued b-metric spaces, Bulletin of Mathematics and Statistics Research, 1(1)(2013), 1-8.
[23] Ullah, N., Shagari, M. S., Azam, A., Fixed Point Theorems in complex valued extended b metric spaces. Moroccan J. of Pure and Appl. Anal. 5(2019), no. 2, 140-163.
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