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On Solvability for Certain Functional Equations Arising in Dynamic Programming

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Mathematics and Computing

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 139))

Abstract

In this paper, we study the existence, uniqueness, and iterative approximations of solutions for the functional equations arising in dynamic programming under Banach spaces and complete metric spaces. Our results unify the results of Bellman [1], Bhakta and Mitra [3], Bhakta and Choudhury [4], Liu [8], Liu and Ume [10], Liu et al. [11], Liu et al. [13], Liu and Kang [9], and Jiang et al. [7]. Examples are provided to support our results.

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References

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Acknowledgments

This work was carried out under the project on Optimization and Reliability Modelling of Indian Statistical Institute. The authors wish to thank the unknown referees who patiently went through the article and whose suggestions considerably improved its presentation and readability.

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Authors and Affiliations

  1. SQC & OR Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata, 700108, India

    Deepmala & A. K. Das

Authors
  1. Deepmala
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  2. A. K. Das
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Correspondence to Deepmala .

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Editors and Affiliations

  1. Department of Mathematics, University of Central Florida, Orlando, Florida, USA

    Ram N. Mohapatra

  2. Indian Institute of Technology Kharagpur Dept. Computer Science & Engineering, Kharagpur, West Bengal, India

    Dipanwita Roy Chowdhury

  3. Dept of Computer Science & Engineering, Haldia Institute of Technology, Haldia, West Bengal, India

    Debasis Giri

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Deepmala, Das, A.K. (2015). On Solvability for Certain Functional Equations Arising in Dynamic Programming. In: Mohapatra, R., Chowdhury, D., Giri, D. (eds) Mathematics and Computing. Springer Proceedings in Mathematics & Statistics, vol 139. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2452-5_6

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