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Fixed Point Construction Processes

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

Assume $\rho \in \Re$ is $(UUC1)$ . Let C be a ρ-closed ρ-bounded convex nonempty subset of $L_{\rho}$ . Let $T: C\rightarrow C$ be a pointwise asymptotically nonexpansive mapping. According to Theorem 5.7 the mapping T has a fixed point. The proof of this important theorem is of the existential nature and does not describe any algorithm for constructing a fixed point of an asymptotic pointwise ρ-nonexpansive mapping. This chapter aims at filling this gap. Therefore, we will define iterative processes for the fixed point construction in modular function spaces and we will prove their convergence. These algorithms will be based on classical iterative methods introduced originally by Mann in [161] and Ishikawa [97], see also Section 2.6 of this book. The results of the current section draw mostly on the research exposed in [54].

Suggested Citation

  • Mohamed A. Khamsi & Wojciech M. Kozlowski, 2015. "Fixed Point Construction Processes," Springer Books, in: Fixed Point Theory in Modular Function Spaces, edition 127, chapter 6, pages 171-184, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-14051-3_6
    DOI: 10.1007/978-3-319-14051-3_6
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