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On Weak Contractive Cyclic Maps in Generalized Metric Spaces and Some Related Results on Best Proximity Points and Fixed Points

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  • M. De la Sen

Abstract

This paper discusses the properties of convergence of sequences to limit cycles defined by best proximity points of adjacent subsets for two kinds of weak contractive cyclic maps defined by composite maps built with decreasing functions with either the so‐called r‐weaker Meir‐Keeler or (r, r0)‐stronger Meir‐Keeler functions in generalized metric spaces. Particular results about existence and uniqueness of fixed points are obtained for the case when the sets of the cyclic disposal have a nonempty intersection. Illustrative examples are discussed.

Suggested Citation

  • M. De la Sen, 2016. "On Weak Contractive Cyclic Maps in Generalized Metric Spaces and Some Related Results on Best Proximity Points and Fixed Points," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnddns:v:2016:y:2016:i:1:n:4186960
    DOI: 10.1155/2016/4186960
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    References listed on IDEAS

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    1. Chi-Ming Chen & Erdal Karapınar & Vladimir Rakočević, 2014. "Existence of Periodic Fixed Point Theorems in the Setting of Generalized Quasi-Metric Spaces," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-8, August.
    2. M. De la Sen & E. Karapinar, 2013. "Best Proximity Points of Generalized Semicyclic Impulsive Self‐Mappings: Applications to Impulsive Differential and Difference Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. A. Kaewcharoen & B. Panyanak, 2008. "Fixed Points for Multivalued Mappings in Uniformly Convex Metric Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2008, pages 1-9, February.
    4. M. De la Sen & E. Karapinar, 2013. "Best Proximity Points of Generalized Semicyclic Impulsive Self-Mappings: Applications to Impulsive Differential and Difference Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-16, October.
    5. Chi-Ming Chen & Erdal Karapınar & Vladimir Rakočević, 2014. "Existence of Periodic Fixed Point Theorems in the Setting of Generalized Quasi‐Metric Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
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