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.

Fishes associated with pelagic Sargassum and open water lacking Sargassum in the Gulf Stream off North Carolina

The community structure of fishes associated with pelagic Sargassum spp. and open water lacking Sargassum was examined during summer and fall cruises, 1999–2003, in the Gulf Stream off North Carolina. Significantly more individual fishes (n= 18,799), representing at least 80 species, were collected from samples containing Sargassum habitat, compared to 60 species (n=2706 individuals) collected from openwater habitat. The majority (96%) of fishes collected in both habitats were juveniles, and planehead filefish (Stephanolepis hispidus) dominated both habitats. Regardless of sampling time (day or night), Sargassum habitat yielded significantly higher numbers of individuals and species compared with open-water collections. Overall, fishes collected by neuston net tows from Sargassum habitat were significantly larger in length than fishes collected from open-water habitat with neuston nets. A significant positive, linear relationship existed between numbers of fishes and the quantity of Sargassum collected by neuston net. Underwater video recordings indicated a layered structure of fishes among and below the algae and that smaller fishes were more closely associated with the algae than larger fishes. Observations of schooling behaviors of filefishes (Monacanthidae), dolphinfish (Coryphaena hippurus), and jacks (Carangidae), and fish-jellyfish associations were also recorded with an underwater video camera. Our data indicate that Sargassum provides a substantial nursery habitat for many juvenile fishes off the U.S. southeast coast.