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

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  • Moosa Gabeleh

    (Ayatollah Boroujerdi University)

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.

Suggested Citation

  • Moosa Gabeleh, 2013. "Proximal Weakly Contractive and Proximal Nonexpansive Non-self-Mappings in Metric and Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 615-625, August.
    • Handle: RePEc:spr:joptap:v:158:y:2013:i:2:d:10.1007_s10957-012-0246-8
    DOI: 10.1007/s10957-012-0246-8
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    References listed on IDEAS

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    1. N. Shahzad & S. Sadiq Basha & R. Jeyaraj, 2011. "Common Best Proximity Points: Global Optimal Solutions," Journal of Optimization Theory and Applications, Springer, vol. 148(1), pages 69-78, January.
    2. S. Sadiq Basha, 2011. "Best Proximity Points: Optimal Solutions," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 210-216, October.
    3. S. Sadiq Basha, 2011. "Best proximity points: global optimal approximate solutions," Journal of Global Optimization, Springer, vol. 49(1), pages 15-21, January.
    4. A. Abkar & M. Gabeleh, 2012. "Global Optimal Solutions of Noncyclic Mappings in Metric Spaces," Journal of Optimization Theory and Applications, Springer, vol. 153(2), pages 298-305, May.
    5. Chirasak Mongkolkeha & Poom Kumam, 2012. "Best Proximity Point Theorems for Generalized Cyclic Contractions in Ordered Metric Spaces," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 215-226, October.
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    Cited by:

    1. Moosa Gabeleh, 2015. "Best Proximity Point Theorems via Proximal Non-self Mappings," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 565-576, February.

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