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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

applied mathematics

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