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On Monotone Mappings in Modular Function Spaces

In: Advances in Metric Fixed Point Theory and Applications

Author

Listed:
  • M. R. Alfuraidan

    (King Fahd University of Petroleum and Minerals, Department of Mathematics and Statistics)

  • M. A. Khamsi

    (University of Texas at El Paso, Department of Mathematical Sciences
    Khalifa University, Department of Applied Mathematics and Sciences)

  • W. M. Kozlowski

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

Abstract

Because of its many diverse applications, fixed point theory has been a flourishing area of mathematical research for decades. Banach’s formulation of the contraction mapping principle in the early twentieth century signaled the advent of an intense interest in the metric related aspects of the theory. The metric fixed point theory in modular function spaces is closely related to the metric theory, in that it provides modular equivalents of norm and metric concepts. Modular spaces are extensions of the classical Lebesgue and Orlicz spaces, and in many instances, conditions cast in this framework are more natural and more easily verified than their metric analogs. In this chapter, we study the existence and construction of fixed points for monotone nonexpansive mappings acting in modular functions spaces equipped with a partial order or a graph structure.

Suggested Citation

  • M. R. Alfuraidan & M. A. Khamsi & W. M. Kozlowski, 2021. "On Monotone Mappings in Modular Function Spaces," Springer Books, in: Yeol Je Cho & Mohamed Jleli & Mohammad Mursaleen & Bessem Samet & Calogero Vetro (ed.), Advances in Metric Fixed Point Theory and Applications, chapter 0, pages 217-240, Springer.
    • Handle: RePEc:spr:sprchp:978-981-33-6647-3_10
    DOI: 10.1007/978-981-33-6647-3_10
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