On Monotone Mappings in Modular Function Spaces

M. R. Alfuraidan (), M. A. Khamsi () and W. M. Kozlowski ()
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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
W. M. Kozlowski: University of New South Wales, School of Mathematics and Statistics

Chapter Chapter 10 in Advances in Metric Fixed Point Theory and Applications, 2021, pp 217-240 from Springer

Abstract: 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.

Keywords: Di-graph; Fibonacci-Mann iteration; Fixed point; Krasnoselskii-Mann iteration; Modular function spaces; Modular uniform convexity; Monotone mappings (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/978-981-33-6647-3_10

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