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An Introduction to Fixed Point Theory in Modular Function Spaces

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Topics in Fixed Point Theory

Abstract

The purpose of this chapter is to give an introduction into the theory of modular function spaces and into the fixed point theory for nonlinear mappings, and semigroups of such mappings, defined on some subsets of such spaces. Modular function spaces are natural generalizations of both function and sequence variants of many important, from applications perspective, spaces like Lebesgue, Orlicz, Musielak–Orlicz, Lorentz, Orlicz–Lorentz, Calderon–Lozanovskii spaces and many others. In the context of the fixed point theory, we will discuss foundations of the geometry of modular function spaces. We will also introduce other important fixed point theory techniques like modular versions type functions and of the Opial property. We will present a series of existence theorems of fixed points for nonlinear mappings, and of common fixed points for semigroups of mappings. We will also touch upon the iterative algorithms for the construction of the fixed points of the asymptotic pointwise nonexpansive mappings and the convergence of such algorithms.

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of New South Wales, Sydney, NSW, 2052, Australia

    W. M. Kozlowski

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  1. W. M. Kozlowski
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Correspondence to W. M. Kozlowski .

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Editors and Affiliations

  1. Department of Mathematics, University of Tabuk, Tabuk, Saudi Arabia

    Saleh Almezel

  2. Department of Mathematics, Aligarh Muslim University, Aligarh, Uttar Pradesh, India

    Qamrul Hasan Ansari

  3. Department of Mathematical Sciences, University of Texas at El Paso, El Paso, Texas, USA

    Mohamed Amine Khamsi

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Kozlowski, W.M. (2014). An Introduction to Fixed Point Theory in Modular Function Spaces. In: Almezel, S., Ansari, Q., Khamsi, M. (eds) Topics in Fixed Point Theory. Springer, Cham. https://doi.org/10.1007/978-3-319-01586-6_5

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