Convergence properties and fixed points of two general iterative schemes with composed maps in Banach spaces with applications to guaranteed global stability. (English) Zbl 1474.54145

De la Sen, Manuel; Ibeas, Asier

Abstr. Appl. Anal. 2014, Article ID 948749, 13 p. (2014).

Summary: This paper investigates the boundedness and convergence properties of two general iterative processes which involve sequences of self-mappings on either complete metric or Banach spaces. The sequences of self-mappings considered in the first iterative scheme are constructed by linear combinations of a set of self-mappings, each of them being a weighted version of a certain primary self-mapping on the same space. The sequences of self-mappings of the second iterative scheme are powers of an iteration-dependent scaled version of the primary self-mapping. Some applications are also given to the important problem of global stability of a class of extended nonlinear polytopic-type parameterizations of certain dynamic systems.

MSC:

54H25	Fixed-point and coincidence theorems (topological aspects)
47J25	Iterative procedures involving nonlinear operators

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