A unifying approach for some nonexpansiveness conditions on modular vector spaces
Articles
Andrea Bejenaru
University Politehnica of Bucharest
https://orcid.org/0000-0003-2741-2243
Mihai Postolache
University Politehnica of Bucharest
https://orcid.org/0000-0003-0738-787X
Published 2020-09-01
https://doi.org/10.15388/namc.2020.25.18044
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Keywords

modular vector space
generalized nonexpansive mappings
condition (C)
condition (E)

How to Cite

Bejenaru A. and Postolache M. (2020) “A unifying approach for some nonexpansiveness conditions on modular vector spaces”, Nonlinear Analysis: Modelling and Control, 25(5), pp. 827–845. doi: 10.15388/namc.2020.25.18044.

Abstract

This paper provides a new, symmetric, nonexpansiveness condition to extend the classical Suzuki mappings. The newly introduced property is proved to be equivalent to condition (E) on Banach spaces, while it leads to an entirely new class of mappings when going to modular vector spaces; anyhow, it still provides an extension for the modular version of condition (C). In connection with the newly defined nonexpansiveness, some necessary and sufficient conditions for the existence of fixed points are stated and proved. They are based on Mann and Ishikawa iteration procedures, convenient uniform convexities and properly selected minimizing sequences.

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