Herb Kunze, Davide La Torre, Franklin Mendivil, Edward R. Vrscay
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
| Davide La Torre |
Department of Economics, Management, and Quantitative Methods
University of Milan, Milan, Italy.
email: firstname.lastname@example.org, email@example.com
| Franklin Mendivil |
Department of Mathematics and Statistics, Acadia University
Wolfville, Nova Scotia, Canada
| Edward R. Vrscay |
Department of Applied Mathematics, Faculty of Mathematics
University of Waterloo, Waterloo, Ontario, Canada
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