Fixed Point Existence Theorems in Modular Function Spaces

Mohamed A. Khamsi () and Wojciech M. Kozlowski ()
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Mohamed A. Khamsi: The University of Texas at El Paso, Department of Mathematical Sciences
Wojciech M. Kozlowski: University of New South Wales, School of Mathematics and Statistics

Chapter 5 in Fixed Point Theory in Modular Function Spaces, 2015, pp 111-169 from Springer

Abstract: 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.

Keywords: Nonexpansive Mapping; Common Fixed Point; Fixed Point Theory; Uniform Convexity; Fixed Point Result (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-14051-3_5

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DOI: 10.1007/978-3-319-14051-3_5

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