G-Contractive Sequential Composite Mapping Theorem in Banach or Probabilistic Banach Space and Application to Prey-Predator System and A & H Stock Prices

Author(s)
Tianquan Yun

ABSTRACT

Theorems of iteration g-contractive sequential composite mapping and periodic mapping in Banach or probabilistic Bannach space are proved, which allow some contraction ratios of the sequence of mapping might be larger than or equal to 1, and are more general than the Banach contraction mapping theorem. Application to the proof of existence of solutions of cycling coupled nonlinear differential equations arising from prey-predator system and A&H stock prices are given.

Theorems of iteration g-contractive sequential composite mapping and periodic mapping in Banach or probabilistic Bannach space are proved, which allow some contraction ratios of the sequence of mapping might be larger than or equal to 1, and are more general than the Banach contraction mapping theorem. Application to the proof of existence of solutions of cycling coupled nonlinear differential equations arising from prey-predator system and A&H stock prices are given.

KEYWORDS

G-Contractive Mapping, Periodic Mapping, Probabilistic Banach Space, Prey-Predator System, Differential Equation of Stock Price

G-Contractive Mapping, Periodic Mapping, Probabilistic Banach Space, Prey-Predator System, Differential Equation of Stock Price

Cite this paper

nullT. Yun, "G-Contractive Sequential Composite Mapping Theorem in Banach or Probabilistic Banach Space and Application to Prey-Predator System and A & H Stock Prices,"*Applied Mathematics*, Vol. 2 No. 6, 2011, pp. 699-704. doi: 10.4236/am.2011.26092.

nullT. Yun, "G-Contractive Sequential Composite Mapping Theorem in Banach or Probabilistic Banach Space and Application to Prey-Predator System and A & H Stock Prices,"

References

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[2] T. Q. Yun, “Fixed Point Theorem of Composition G-Conaction Mapping and Its Applications,” Applied Mathematics and Mechanics, Vol. 22, No. 10, 2001, pp. 1132-1139. doi:10.1023/A:1016337014775

[3] J. S. Yu, T.Q. Yun and Z. M. Guo, “Theory of Computational Securities,” In Chinese, Scientific Publication House, Beijing, 2008.

[4] T. Q. Yun and G. L. Lei, “Simplest Differential Equation of Stock Price, Its Solution and Relation to Assumption of Black-Scholes Model,” Applied Mathematics and Mechanics, Vol. 24, No. 6, 2003, pp. 654-658. doi:10.1007/BF02437866

[5] C. W. Gardiner, “Handbook of Stochastic Methods, for Physics, Chemistry and the Natural Sciences,” Springer- Verlag Press, Berlin, 1983.

[6] T. Q. Yun and T. Yun, “Simple Differential Equations of A & H Stock Prices and Application to Analysis of Equilibrium State,” Technology and Investment, Vol. 1, No. 2, 2010, pp. 111-114. doi:10.4236/ti.2010.12013

[1] A. T. Bharucha-Reid, “Fixed Point Theorems in Probabilistic Analysis,” Bulletin of the American Mathematical Society, Vol. 83, No. 5, 1976, pp. 641-657. doi:10.1090/S0002-9904-1976-14091-8

[2] T. Q. Yun, “Fixed Point Theorem of Composition G-Conaction Mapping and Its Applications,” Applied Mathematics and Mechanics, Vol. 22, No. 10, 2001, pp. 1132-1139. doi:10.1023/A:1016337014775

[3] J. S. Yu, T.Q. Yun and Z. M. Guo, “Theory of Computational Securities,” In Chinese, Scientific Publication House, Beijing, 2008.

[4] T. Q. Yun and G. L. Lei, “Simplest Differential Equation of Stock Price, Its Solution and Relation to Assumption of Black-Scholes Model,” Applied Mathematics and Mechanics, Vol. 24, No. 6, 2003, pp. 654-658. doi:10.1007/BF02437866

[5] C. W. Gardiner, “Handbook of Stochastic Methods, for Physics, Chemistry and the Natural Sciences,” Springer- Verlag Press, Berlin, 1983.

[6] T. Q. Yun and T. Yun, “Simple Differential Equations of A & H Stock Prices and Application to Analysis of Equilibrium State,” Technology and Investment, Vol. 1, No. 2, 2010, pp. 111-114. doi:10.4236/ti.2010.12013