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Some Results on Fixed and Best Proximity Points of Multivalued Cyclic Self‐Mappings with a Partial Order

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  • M. De la Sen

Abstract

This paper is devoted to investigate the fixed points and best proximity points of multivalued cyclic self‐mappings on a set of subsets of complete metric spaces endowed with a partial order under a generalized contractive condition involving a Hausdorff distance. The existence and uniqueness of fixed points of both the cyclic self‐mapping and its associate composite self‐mappings on each of the subsets are investigated, if the subsets in the cyclic disposal are nonempty, bounded and of nonempty convex intersection. The obtained results are extended to the existence of unique best proximity points in uniformly convex Banach spaces.

Suggested Citation

  • M. De la Sen, 2013. "Some Results on Fixed and Best Proximity Points of Multivalued Cyclic Self‐Mappings with a Partial Order," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:968492
    DOI: 10.1155/2013/968492
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    References listed on IDEAS

    as
    1. Shyam Lal Singh & Swami Nath Mishra & Renu Chugh & Raj Kamal, 2012. "General Common Fixed Point Theorems and Applications," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
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    6. Yonghong Yao & Muhammad Aslam Noor & Yeong-Cheng Liou & Shin Min Kang, 2012. "Iterative Algorithms for General Multivalued Variational Inequalities," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-10, December.
    7. Shyam Lal Singh & Swami Nath Mishra & Renu Chugh & Raj Kamal, 2012. "General Common Fixed Point Theorems and Applications," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, February.
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