Abstract
In this chapter, we introduce the new concept of the joint common limit in the range property (shortly, (JCLR)-property) in \(S_b\)-metric spaces and prove some common fixed point theorems by using the JCLR-property in \(S_b\)-metric spaces without the completeness of \(S_b\)-metric spaces. We also give some examples to illustrate our results. As applications of our results, we show the existence of common solutions for a system of functional equations in dynamic programming.
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References
Czerwik, S.: Contraction mappings in \(b\) -metric spaces. Acta Math. Inform. Univ. Ostraviensis 1, 5–11 (1993)
Cho, Y.J.: Survey on Metric Fixed Point Theory and Applications. Advances on Real and Complex Analysis with Applications, Trends in Mathematics. Ruzhahsky, M., Cho, Y.J., Agarwal, P., Area, I., (eds.). Birkhäuser, Springer (2017)
Boriceanu, M., Bota, M., Petrusel, A.: Mutivalued fractals in \(b\) -metric spaces. Cent. Europ. J. Math. 8, 367–377 (2010)
Bota, M., Molnar, A., Csaba, V.: On Ekeland’s variational principle in \(b\) -metric spaces. Fixed Point Theory 12, 21–28 (2011)
Czerwik, S.: Nonlinear set-valued contraction mappings in \(b\) -metric spaces. Atti Semin. Mat. Fis. Univ. Modena 46, 263–276 (1998)
Sedghi, S., Shobe, N., Došenović, T.: Fixed point results in \(S\) -metric spaces. Nonlinear Funct. Anal. Appl. 20, 55–67 (2015)
Sedghi, S., Gholidahneh, A., Došenović, T., Esfahani, J., Randenović, S.: Common fixed point of four maps in \(S_b\) -metric spaces. J. Linear Topol. Algebra 5, 93–104 (2016)
Bellman, R., Lee, E.S.: Functional equations in dynamic programming. Aequat. Math. 17, 1–18 (1978)
Bhakta, T.C., Mitra, S.: Some existence theorems for functional equations arising in dynamic programming. J. Math. Anal. Appl. 98, 348–362 (1984)
Liu, Z., Wang, L., Kim, H.K., Kang, S.M.: Common fixed point theorems for contractive type mapping and their applications in dynamic programming. Bull. Korean Math. Soc. 45, 573–585 (2008)
Pathak, H.K., Cho, Y.J., Kang, S.M., Lee, B.S.: Fixed point theorems for compatible mapping of type \((P)\) and applications to dynamic programming. Le Mate. 50, 15–33 (1995)
Zhang, S.S.: Some existence theorems of common and coincidence solutions for a class of functional equations arising in dynamic programming. Appl. Math. Mech. 12, 31–37 (1991)
Acknowledgements
This work was supported by Thammasat University Research Unit in Fixed Points and Optimization. This work was partially completed while the first and second authors visited the Department of Mathematics Education, Gyeongsang National University, Korea.
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Yamaod, O., Sintunavarat, W., Cho, Y.J. (2021). Common Solutions for a System of Functional Equations in Dynamic Programming Passing Through the JCLR-Property in \(S_b\)-Metric Spaces. In: Cho, Y.J., Jleli, M., Mursaleen, M., Samet, B., Vetro, C. (eds) Advances in Metric Fixed Point Theory and Applications. Springer, Singapore. https://doi.org/10.1007/978-981-33-6647-3_19
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DOI: https://doi.org/10.1007/978-981-33-6647-3_19
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