Fixed Points of Closed and Compact Composite Sequences of Operators and Projectors in a Class of Banach Spaces

Some results on fixed points related to the contractive compositions of bounded operators in a class of complete metric spaces which can be also considered as Banach's spaces are discussed through the paper. The class of composite operators under study can include, in particular, sequences of projection operators under, in general, oblique projective operators. In this paper we are concerned with composite operators which include sequences of pairs of contractive operators involving, in general, oblique projection operators. The results are generalized to sequences of, in general, nonconstant bounded closed operators which can have bounded, closed, and compact limit operators, such that the relevant composite sequences are also compact operators. It is proven that in both cases, Banach contraction principle guarantees the existence of unique fixed points under contractive conditions.

Size and year class composition of catch, age and growth of yellowfin tuna in the Eastern Tropical Pacific Ocean for the years 1954-1958

ENGLISH: Data on the size composition of catch for the years 1954-1958 have been studied to determine year class composition, age and growth of yellowfin tuna in the Eastern Tropical Pacific Ocean. Direct age determination of tropical tunas has not yet proven reliable; however, this analysis has shown that the length-frequency distributions themselves are adequate to determine year class structure and growth rates. Absolute age has been estimated by comparing the average time of spawning with the time at which age groups initially appear in the catch. SPANISH: Los datos sobre la composición del tamaño de la pesca durante los años 1954-1958 han sido estudiados con el objeto de determinar la composición de las clases anuales, la edad y el crecimiento del atún aleta amarilla en el Océano Pacífico Oriental Tropical. Las determinaciones directas de la edad de los atunes tropicales no han probado todavía ser de confianza; sin embargo, este análisis ha demostrado que las distribuciones de la frecuencia de las longitudes son adecuadas para determinar la estructura de las clases anuales y de las tasas de crecimiento. La edad absoluta ha sido estimada mediante la comparación de la época promedio de desove con la epoca en que los grupos de edades comienzan a aparecer en la pesca.