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16
Generation theory for semigroups of holomorphic mappings in Banach spaces
 Abstr. Appl. Anal
, 1996
"... Abstract. We study nonlinear semigroups ofholomorphic mappings in Banach spaces and their infinitesimal generators. Using resolvents, we characterize, in particular, bounded holomorphic generators on bounded convex domains and obtain an analog ofthe Hille exponential formula. We then apply our resul ..."
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Cited by 11 (10 self)
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Abstract. We study nonlinear semigroups ofholomorphic mappings in Banach spaces and their infinitesimal generators. Using resolvents, we characterize, in particular, bounded holomorphic generators on bounded convex domains and obtain an analog ofthe Hille exponential formula. We then apply our results to the null point theory ofsemiplus complete vector fields. We study the structure ofnull point sets and the spectral characteristics of null points, as well as their existence and uniqueness. A global version of the implicit function theorem and a discussion of some open problems are also included.
Proof Interpretations and the Computational Content of Proofs. Draft of book in preparation
, 2007
"... This survey reports on some recent developments in the project of applying proof theory to proofs in core mathematics. The historical roots, however, go back to Hilbert’s central theme in the foundations of mathematics which can be paraphrased by the following question ..."
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Cited by 9 (1 self)
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This survey reports on some recent developments in the project of applying proof theory to proofs in core mathematics. The historical roots, however, go back to Hilbert’s central theme in the foundations of mathematics which can be paraphrased by the following question
Asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces, arXiv:0707.1626v2 [math.FA
 J. of the European Math. Soc
, 2007
"... This paper provides a fixed point theorem for asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces as well as new effective results on the KrasnoselskiMann iterations of such mappings. The latter were found using methods from logic and the paper continues a case study in the g ..."
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Cited by 8 (7 self)
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This paper provides a fixed point theorem for asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces as well as new effective results on the KrasnoselskiMann iterations of such mappings. The latter were found using methods from logic and the paper continues a case study in the general program of extracting effective data from primafacie ineffective proofs in the fixed point theory of such mappings. 1
The approximate fixed point property in product spaces, Nonlinear Analysis 66
, 2007
"... spaces ..."
Center for Applied Mathematical Sciences
 in Differential Equations with Applications
, 1991
"... We present new convergence and stability results for least squares inverse problems involving systems described by analytic semigroups. The practical importance of these results is demonstrated by application to several examples from problems of estimation of material parameters in flexible structur ..."
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We present new convergence and stability results for least squares inverse problems involving systems described by analytic semigroups. The practical importance of these results is demonstrated by application to several examples from problems of estimation of material parameters in flexible structures using accelerometer data. 1 This research was supported in part by the Air Force Office of Scientific Research under Contract F4962086C0111, by the National Aeronautics and Space Administration under NASA Grant NAG1517, and by the National Science Foundation under NSF Grant DMS8818530. Part of this research was carried out while the first author was a visiting scientist at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA, which is operated under NASA contract NAS118605. 2 Invited Lecture, International Conference on Differential Equations and Applications, Retzhof, Austria, June 1824, 1989. 1. Introduction ...
TWO GENERIC RESULTS IN FIXED POINT THEORY
"... Abstract. We give two examples of the generic approach to fixed point theory. The first example is concerned with the asymptotic behavior of infinite products of nonexpansive mappings in Banach spaces and the second with the existence and stability of fixed points of continuous mappings in finitedi ..."
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Abstract. We give two examples of the generic approach to fixed point theory. The first example is concerned with the asymptotic behavior of infinite products of nonexpansive mappings in Banach spaces and the second with the existence and stability of fixed points of continuous mappings in finitedimensional Euclidean spaces. 1.
Genericity and Porosity in Nonlinear Analysis and Optimization
, 2005
"... We present several recent examples of the generic approach to nonlinear problems. In this approach, instead of considering, for instance, the convergence of an algorithm, one investigates an appropriate space of algorithms equipped with some natural complete metric and shows that convergence does in ..."
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We present several recent examples of the generic approach to nonlinear problems. In this approach, instead of considering, for instance, the convergence of an algorithm, one investigates an appropriate space of algorithms equipped with some natural complete metric and shows that convergence does indeed occur for most algorithms there. As we shall see, sometimes one can show that the complement of the good
Nonexpansive Retracts in Banach Spaces
, 1787
"... We study various aspects of nonexpansive retracts and retractions in certain Banach and metric spaces, with special emphasis on the compact nonexpansive envelope property. ..."
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We study various aspects of nonexpansive retracts and retractions in certain Banach and metric spaces, with special emphasis on the compact nonexpansive envelope property.
Supported by the Austrian Federal Ministry of Education, Science and Culture
"... We first characterize ρmonotone mappings on the Hilbert ball by using their resolvents and then study the asymptotic behavior of compositions and convex combinations of these resolvents. ..."
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We first characterize ρmonotone mappings on the Hilbert ball by using their resolvents and then study the asymptotic behavior of compositions and convex combinations of these resolvents.