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Báo cáo hóa học: "Research Article Common Fixed Point and Approximation Results for Noncommuting Maps on Locally Convex 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: Research Article Common Fixed Point and Approximation Results for Noncommuting Maps on Locally Convex Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 207503 14 pages doi 10.1155 2009 207503 Research Article Common Fixed Point and Approximation Results for Noncommuting Maps on Locally Convex Spaces F. Akbar1 and A. R. Khan2 1 Department of Mathematics University ofSargodha Sargodha Pakistan 2 Department of Mathematics and Statistics King Fahd University of Petroleum Minerals Dhahran 31261 Saudi Arabia Correspondence should be addressed to A. R. Khan arahim@kfupm.edu.sa Received 21 February 2009 Accepted 14 April 2009 Recommended by Anthony Lau Common fixed point results for some new classes of nonlinear noncommuting maps on a locally convex space are proved. As applications related invariant approximation results are obtained. Our work includes improvements and extension of several recent developments of the existing literature on common fixed points. We also provide illustrative examples to demonstrate the generality of our results over the known ones. Copyright 2009 F. Akbar and A. R. Khan. 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 and Preliminaries In the sequel E T will be a Hausdorff locally convex topological vector space. A family pa a 6 I of seminorms defined on E is said to be an associated family of seminorms for T if the family I U Y 0 where U n 1Uai and Uai x pai x 1 forms a base of neighborhoods of zero for T. A family pa a 6 I of seminorms defined on E is called an augmented associated family for T if pa a 6 I is an associated family with property that the seminorm max pa pp 6 pa a 6 I for any a p 6 I. The associated and augmented associated families of seminorms will be denoted by A t and A t respectively. It is well known that given a locally convex space E T there always exists a family pa a 6 I of seminorms defined on E such