Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability

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.

Subsurface Fish Handling to Limit Decompression Effects on Deepwater Species

A method of handling hooked fish at intermediate depth was developed for species which occur deeper than conventional scuba depths. Juvenile pink snappers, Pristipomoides filamentosus, were hauled from 65-100 m to a depth of only 30 m, where the ambient pressure change was a fraction of that produced by hauling fish to the sea surface. This method afforded a unique opportunity to acoustically tag deepwater, physoclistous fish without the need to alter the fish's original swim bladder volume and without the high risk of further injury associated with surface handling. Tagged P. filamentosus survived and behaved well and were tracked successfully. This basic method could be applied to a variety of deepwater species in a number of research approaches, including tagging and dietary studies.