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On the solution of the traumatic avoidance learning model approached by the Banach fixed point theorem

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Abstract

This paper deals with a specific type of traumatic avoidance for the learning process of normal dogs enclosed into a small compartment with a steel grid floor. Our aim is to analyze the behavior of the dogs in such situations and to construct a suitable mathematical model for it. The existence and uniqueness results of the proposed traumatic avoidance learning model are being investigated by the use of the Banach fixed point theorem.

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References

  1. Aoki, T.: On the stability of the linear transformation in Banach spaces. J. Math. Soc. Jpn. 2, 64–66 (1950)

    Article  MathSciNet  Google Scholar 

  2. Banach, S.: Sur les operations dans les ensembles abstraits et leur applications aux equations integrales. Fund. Math. 3, 133–181 (1922)

    Article  MathSciNet  Google Scholar 

  3. Gavruta, P.: A generalization of the Hyers–Ulam–Rassias stability of approximately additive mappings. J. Math. Anal. Appl. 184, 431–436 (1994)

    Article  MathSciNet  Google Scholar 

  4. Hilgard, E.R., Marquis, D.G.: Conditioning and Learning, pp. 58–62. D. Appleton-Century, New York (1940)

    Google Scholar 

  5. Hyers, D.H.: On the stability of the linear functional equation. Proc. Nat. Acad. Sci. USA 27, 222–224 (1941)

    Article  MathSciNet  Google Scholar 

  6. Hyers, D.H., Isac, G., Rassias, ThM: Stability of Functional Equations in Several Variables. Birkhauser, Basel (1998)

    Book  Google Scholar 

  7. Keller, F.S., Schoenfeld, W.N.: Principles of Psychology, pp. 311–315. Appleton-Century-Crofts, New York (1950)

    Google Scholar 

  8. Miller, N.E.: Learnable drives and rewards. In: Stevens, S.S. (ed.) Handbook of Experimental Psychology, pp. 435–472. Wiley, New York (1951)

    Google Scholar 

  9. Nash Jr., J.F., Rassias, T.M. (eds.): Open Problems in Mathematics. Springer, New York (2016)

    MATH  Google Scholar 

  10. Solomon, R.L., Wynne, L.C.: Traumatic avoidance learning: acquisition in normal dogs. Psychol. Monogr., 67, No. 4 (Whole No. 354) (1953)

  11. Turab, A., Sintunavarat, W.: On analytic model for two-choice behavior of the paradise fish based on the fixed point method. J. Fixed Point Theory Appl. 21, 56 (2019). https://doi.org/10.1007/s11784-019-0694-y

    Article  MathSciNet  MATH  Google Scholar 

  12. Ulam, S.M.: A Collection of the Mathematical Problems. Interscience Publ, New York (1960)

    MATH  Google Scholar 

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Acknowledgements

The second author would like to thank the Thailand Research Fund and Office of the Higher Education Commission under Grant no. MRG6180283 for financial support during the preparation of this manuscript.

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All authors contributed equally and significantly in writing this paper. All authors read and approved the final manuscript.

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Correspondence to Wutiphol Sintunavarat.

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Turab, A., Sintunavarat, W. On the solution of the traumatic avoidance learning model approached by the Banach fixed point theorem. J. Fixed Point Theory Appl. 22, 50 (2020). https://doi.org/10.1007/s11784-020-00788-3

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  • DOI: https://doi.org/10.1007/s11784-020-00788-3

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