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Fixed and Best Proximity Points of Cyclic Jointly Accretive and Contractive Self‐Mappings

Author

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  • M. De la Sen

Abstract

p(≥2)‐cyclic and contractive self‐mappings on a set of subsets of a metric space which are simultaneously accretive on the whole metric space are investigated. The joint fulfilment of the p‐cyclic contractiveness and accretive properties is formulated as well as potential relationships with cyclic self‐mappings in order to be Kannan self‐mappings. The existence and uniqueness of best proximity points and fixed points is also investigated as well as some related properties of composed self‐mappings from the union of any two adjacent subsets, belonging to the initial set of subsets, to themselves.

Suggested Citation

  • M. De la Sen, 2012. "Fixed and Best Proximity Points of Cyclic Jointly Accretive and Contractive Self‐Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:817193
    DOI: 10.1155/2012/817193
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    References listed on IDEAS

    as
    1. Yonghong Yao & Shin Min Kang & Wu Jigang & Pei-Xia Yang, 2012. "A Regularized Gradient Projection Method for the Minimization Problem," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-9, February.
    2. Vadim Azhmyakov, 2009. "Convexity of the Set of Fixed Points Generated by Some Control Systems," Journal of Applied Mathematics, Hindawi, vol. 2009, pages 1-14, October.
    3. Yonghong Yao & Shin Min Kang & Wu Jigang & Pei-Xia Yang, 2012. "A Regularized Gradient Projection Method for the Minimization Problem," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    4. Vadim Azhmyakov, 2009. "Convexity of the Set of Fixed Points Generated by Some Control Systems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2009(1).
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    Cited by:

    1. M. De la Sen, 2013. "On a Class of Self‐Adjoint Compact Operators in Hilbert Spaces and Their Relations with Their Finite‐Range Truncations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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