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Fixed Point Existence Theorems in Modular Function Spaces

In: Fixed Point Theory in Modular Function Spaces

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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 presents a series of fixed point existence theorems for nonlinear mappings acting in modular functions spaces. We cover a range of different types of mappings including ρ-contractions and their pointwise asymptotic versions and ρ-nonexpansive mappings and pointwise asymptotic ρ-nonexpansive mappings, under various assumptions on the function modular ρ and on the sets these mappings are defined in. In addition we will discuss some examples and applications to the theory of differential equations.

Suggested Citation

  • Mohamed A. Khamsi & Wojciech M. Kozlowski, 2015. "Fixed Point Existence Theorems in Modular Function Spaces," Springer Books, in: Fixed Point Theory in Modular Function Spaces, edition 127, chapter 5, pages 111-169, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-14051-3_5
    DOI: 10.1007/978-3-319-14051-3_5
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