tailieunhanh - Báo cáo hóa học: " CONTINUATION THEORY FOR GENERAL CONTRACTIONS IN GAUGE SPACES"

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: CONTINUATION THEORY FOR GENERAL CONTRACTIONS IN GAUGE SPACES | CONTINUATION THEORY FOR GENERAL CONTRACTIONS IN GAUGE SPACES ADELA CHIS AND RADU PRECUP Received 9 March 2004 and in revised form 30 April 2004 A continuation principle of Leray-Schauder type is presented for contractions with respect to a gauge structure depending on the homotopy parameter. The result involves the most general notion of a contractive map on a gauge space and in particular yields homotopy invariance results for several types of generalized contractions. 1. Introduction One of the most useful results in nonlinear functional analysis the Banach contraction principle states that every contraction on a complete metric space into itself has a unique fixed point which can be obtained by successive approximations starting from any element of the space. Further extensions have tried to relax the metrical structure of the space its completeness or the contraction condition itself. Thus there are known versions of the Banach fixed point theorem for contractions defined on subsets of locally convex spaces Marinescu 18 page 181 in gauge spaces spaces endowed with a family of pseudometrics Colojoara 5 and Gheorghiu 11 in uniform spaces Knill 16 and in syntopogenous spaces Precup 21 . As concerns the completeness of the space there are known results for a space endowed with two metrics or more generally with two families of pseudometrics . The space is assumed to be complete with respect to one of them while the contraction condition is expressed in terms of the second one. The first result in this direction is due to Maia 17 . The extensions of Maia s result to gauge spaces with two families of pseudometrics and to spaces with two syntopogenous structures were given by Gheorghiu 12 and Precup 22 respectively. As regards the contraction condition several results have been established for various types of generalized contractions on metric spaces. We only refer to the earlier papers of Kannan 15 Reich 27 Rus 29 and Ciric 4 and to the survey article of Rhoades 28