Herb Kunze, Davide La Torre, Franklin Mendivil, Edward R. Vrscay
Abstract:
Let T be a set-valued contraction mapping on a general Banach space
.
In the first part of this paper we introduce the evolution
inclusion
and study the convergence of solutions
to this inclusion toward fixed points of T.
Two cases are examined:
(i) T has a fixed point
in the usual sense, i.e.,
and
(ii) T has a fixed point in the sense of inclusions, i.e.,
.
In the second part we extend this analysis to the case of set-valued
evolution equations taking the form
.
We also provide some applications to generalized fractal transforms.
Submitted July 16, 2013. Published June 18, 2014.
Math Subject Classifications: 34A60, 28A80.
Key Words: Set-valued evolution inclusions, set-valued evolution equations,
contractive set-valued functions, fixed points.
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Herb Kunze Department of Mathematics and Statistics University of Guelph, Guelph, Ontario, Canada email: hkunze@uoguelph.ca | |
Davide La Torre Department of Economics, Management, and Quantitative Methods University of Milan, Milan, Italy. email: davide.latorre@unimi.it, davide.latorre@kustar.ac.ae | |
Franklin Mendivil Department of Mathematics and Statistics, Acadia University Wolfville, Nova Scotia, Canada email: franklin.mendivil@acadiau.ca | |
Edward R. Vrscay Department of Applied Mathematics, Faculty of Mathematics University of Waterloo, Waterloo, Ontario, Canada email: ervrscay@uwaterloo.ca |
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