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Proximal Weakly Contractive and Proximal Nonexpansive Non-self-Mappings in Metric and Banach Spaces

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Abstract

In this work, we consider two classes of non-self-mappings, which are called proximal weakly contractive and proximal nonexpansive mappings, and study the existence of solutions of a minimization problem. Existence results of best proximity points for these two classes of non-self-mappings in metric and Banach spaces are also obtained.

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Acknowledgements

The author thanks anonymous referees and the handling editor, professor Franco Giannessi, for their helpful remarks and suggestions that allowed him to improve the original presentation.

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  1. Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran

    Moosa Gabeleh

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  1. Moosa Gabeleh
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Correspondence to Moosa Gabeleh.

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Gabeleh, M. Proximal Weakly Contractive and Proximal Nonexpansive Non-self-Mappings in Metric and Banach Spaces. J Optim Theory Appl 158, 615–625 (2013). https://doi.org/10.1007/s10957-012-0246-8

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  • DOI: https://doi.org/10.1007/s10957-012-0246-8

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