tailieunhanh - Báo cáo hóa học: " Research Article A Dual of the Compression-Expansion Fixed Point Theorems"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article A Dual of the Compression-Expansion Fixed Point Theorems | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2007 Article ID 90715 11 pages doi 2007 90715 Research Article A Dual of the Compression-Expansion Fixed Point Theorems Richard Avery Johnny Henderson and Donal O Regan Received 5 June 2007 Accepted 11 September 2007 Recommended by William Art Kirk This paper presents a dual of the fixed point theorems of compression and expansion of functional type as well as the original Leggett-Williams fixed point theorem. The multivalued situation is also discussed. Copyright 2007 Richard Avery et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction In this paper we present a dual of the fixed point theorems of expansion and compression using an axiomatic index theory as well as the original Leggett-Williams fixed point which is itself a generalization of the fixed point theorems of expansion and compression. In 1 Leggett and Williams presented criteria which guaranteed the existence of a fixed point for single-valued continuous compact maps that did not require the operator to be invariant on the underlying sets utilizing a concave functional and the norm. In that sense the Leggett-Williams fixed point theorem generalized the compression-expansion fixed point theorem of norm type by Guo 2 . In 3 Anderson and Avery generalized the fixed point theorem of Guo 2 by replacing the norm in places by convex functionals and in 4 Zhang and Sun extended this result by showing that a certain set was a retract thus completely removing the norm from the argument. In this paper we provide in a sense a generalization of all of the compression-expansion arguments that have utilized the norm and or functionals including 2-6 which does not require sets to be invariant under our operator and yet maintains the freedom gained by using concave