AN EXTENSION OF CANTOR'S INTERSECTION THEOREM AND WELL POSEDNESS OF THE FIXED POINT PROBLEM FOR DISCONTINUOUS MAPPINGS

作者：Jachymski Jacek^*

来源：Journal of Nonlinear and Convex Analysis, 2018, 19(6): 995-1004.

• Intersection theorem
• fixed point
• epsilon-fixed point
• well posedness of the fixed point problem
• Ciric's contraction
• Picard operator
• asymptotically regular mapping

We establish a simple extension of Cantor's intersection theorem in which we weaken the assumption that all sets are closed. This result leads to a characterization of a class of mappings (not necessarily continuous) for which the fixed point problem is well posed. We also present an example of a mapping from that class for which the existence of a fixed point cannot be deduced from the classical Cantor's intersection theorem whereas our result is applicable.

• 出版日期2018