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Geometry of Modular Function Spaces

In: Fixed Point Theory in Modular Function Spaces

Author

Listed:
  • Mohamed A. Khamsi

    (The University of Texas at El Paso, Department of Mathematical Sciences
    King Fahd University of Petroleum & Minerals, Department of Mathematics & Statistics)

  • Wojciech M. Kozlowski

    (University of New South Wales, School of Mathematics and Statistics)

Abstract

This chapter introduces general notions related to the geometry of modular function spaces. We define the modular version of uniform convexity and property (R) which will equip us with powerful tools for proving the fixed point theorems in modular function spaces. The geometrical theory also provides a set of powerful techniques for proving existence of common fixed points for commutative families of mappings acting in modular function spaces, and for investigating the topological properties of the set of common fixed points.

Suggested Citation

  • Mohamed A. Khamsi & Wojciech M. Kozlowski, 2015. "Geometry of Modular Function Spaces," Springer Books, in: Fixed Point Theory in Modular Function Spaces, edition 127, chapter 4, pages 79-109, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-14051-3_4
    DOI: 10.1007/978-3-319-14051-3_4
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