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 Stable Iteration Procedures in Metric Spaces which Generalize a Picard-Type Iteration | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 953091 15 pages doi 2010 953091 Research Article Stable Iteration Procedures in Metric Spaces which Generalize a Picard-Type Iteration M. De la Sen IIDP Faculty of Science and Technology University of the Basque Country Campus of Leioa Bizkaia Aptdo. 644 Bilbao Spain Correspondence should be addressed to M. De la Sen Received 25 March 2010 Accepted 11 July 2010 Academic Editor Dominguez Benavides Copyright 2010 M. De la Sen. 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. This paper investigates the stability of iteration procedures defined by continuous functions acting on self-maps in continuous metric spaces. Some of the obtained results extend the contraction principle to the use of altering-distance functions and extended altering-distance functions the last ones being piecewise continuous. The conditions for the maps to be contractive for the achievement of stability of the iteration process can be relaxed to the fulfilment of being large contractions or to be subject to altering-distance functions or extended altering functions. 1. Introduction Banach contraction principle is a very basic and useful result of Mathematical Analysis 1-7 . Basic applications of this principle are related to stability of both continuous-time and discrete-time dynamic systems 4 8 including the case of high-complexity models for dynamic systems consisting of functional differential equations by the presence of delays 4 9 . Several generalizations of the contraction principle are investigated in 2 by proving that the result still holds if altering-distance functions 1 are replaced with a difference of two continuous monotone nondecreasing real functions which take zero values only at the origin. The .
