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Existence and Approximation of Fixed Points of Bregman Firmly Nonexpansive Mappings in Reflexive Banach Spaces

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Fixed-Point Algorithms for Inverse Problems in Science and Engineering

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 49))

Abstract

We study the existence and approximation of fixed points of Bregman firmly nonexpansive mappings in reflexive Banach spaces.

AMS 2010 Subject Classification: 46T99, 47H04, 47H05, 47H09, 47H10, 47J05, 47J25, 49J40

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Acknowledgements

The first author was partially supported by the Israel Science Foundation (Grant 647/07), by the Fund for the Promotion of Research at the Technion and by the Technion President’s Research Fund. Both authors are grateful to the referees for many detailed and helpful comments.

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Authors and Affiliations

  1. Department of Mathematics, The Technion – Israel Institute of Technology, 32000, Haifa, Israel

    Simeon Reich

Authors
  1. Simeon Reich
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  2. Shoham Sabach
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Correspondence to Simeon Reich .

Editor information

Editors and Affiliations

  1. Okanagan Campus, Department of Mathematics and Statistic, University of British Columbia, Kelowna, V1V 1V7, British Columbia, Canada

    Heinz H. Bauschke

  2. School of Mathematics & Statistics, Division of Information Technology, University of South Australia, Mawson Lakes Blvd., Mawson Lakes, 5095, South Australia, Australia

    Regina S. Burachik

  3. Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Place Jussieu 4, Paris, 75005, France

    Patrick L. Combettes

  4. Dept. Physics, Lab. Atomic & Solid State, Cornell University, Clark Hall, Ithaca, 14853-2501, New York, USA

    Veit Elser

  5. Institut für Numerische und Angewandte M, Universität Göttingen, Lotzestr. 16-18, Göttingen, 37073, Germany

    D. Russell Luke

  6. Faculty of Mathematics, Dept. Combinatorics & Optimization, University of Waterloo, Waterloo, N2L 3G1, Ontario, Canada

    Henry Wolkowicz

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Reich, S., Sabach, S. (2011). Existence and Approximation of Fixed Points of Bregman Firmly Nonexpansive Mappings in Reflexive Banach Spaces. In: Bauschke, H., Burachik, R., Combettes, P., Elser, V., Luke, D., Wolkowicz, H. (eds) Fixed-Point Algorithms for Inverse Problems in Science and Engineering. Springer Optimization and Its Applications(), vol 49. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9569-8_15

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