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On a General Contractive Condition for Cyclic Self‐Mappings

Author

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  • M. De la Sen

Abstract

This paper is concerned with p(≥2)‐cyclic self‐mappings T:⋃i∈p¯ Ai→⋃i∈p¯ Ai in a metric space (X, d), with Ai ⊂ X, T(Ai)⊆Ai+1 for i = 1, 2, …, p, under a general contractive condition which includes as particular cases several of the existing ones in the literature. The existence and uniqueness of fixed points and best proximity points is discussed as well as the convergence to them of the iterates generated by the self‐mapping from given initial points.

Suggested Citation

  • M. De la Sen, 2011. "On a General Contractive Condition for Cyclic Self‐Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
    • Handle: RePEc:wly:jnljam:v:2011:y:2011:i:1:n:542941
    DOI: 10.1155/2011/542941
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    References listed on IDEAS

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    1. 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.
    2. J. Harjani & B. López & K. Sadarangani, 2010. "A Fixed Point Theorem for Mappings Satisfying a Contractive Condition of Rational Type on a Partially Ordered Metric Space," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    3. 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).
    4. J. Harjani & B. López & K. Sadarangani, 2010. "A Fixed Point Theorem for Mappings Satisfying a Contractive Condition of Rational Type on a Partially Ordered Metric Space," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-8, September.
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