Approximating fixed points of \(\left( \lambda ,\rho \right) \)-firmly nonexpansive mappings in modular function spaces

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Abstract

In this paper, we first introduce an iterative process in modular function spaces and then extend the idea of a \(\lambda \)-firmly nonexpansive mapping from Banach spaces to modular function spaces. We call such mappings as \( \left( \lambda ,\rho \right) \)-firmly nonexpansive mappings. We incorporate the two ideas to approximate fixed points of \(\left( \lambda ,\rho \right) \) -firmly nonexpansive mappings using the above-mentioned iterative process in modular function spaces.

Mathematics Subject Classification

46A80 47H09 47H10 

Notes

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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Mathematics, Statistics and PhysicsQatar UniversityDohaQatar

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