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Best Proximity Point Theorems for Some New Cyclic Mappings

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Listed:
  • Chi-Ming Chen
  • Chao-Hung Chen

Abstract

By using the stronger Meir‐Keeler mapping, we introduce the concepts of the sMK‐G‐cyclic mappings, sMK‐K‐cyclic mappings, and sMK‐C‐cyclic mappings, and then we prove some best proximity point theorems for these various types of contractions. Our results generalize or improve many recent best proximity point theorems in the literature (e.g., Elderd and Veeramani, 2006; Sadiq Basha et al., 2011).

Suggested Citation

  • Chi-Ming Chen & Chao-Hung Chen, 2012. "Best Proximity Point Theorems for Some New Cyclic Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:643729
    DOI: 10.1155/2012/643729
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    References listed on IDEAS

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    1. S. Sadiq Basha & N. Shahzad & R. Jeyaraj, 2011. "Optimal Approximate Solutions of Fixed Point Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    2. S. Sadiq Basha & N. Shahzad & R. Jeyaraj, 2011. "Optimal Approximate Solutions of Fixed Point Equations," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-9, July.
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    Cited by:

    1. Shengquan Weng & Hongying Xiao, 2025. "Related Fixed Point Results for LB3S2‐Type Cyclic Mapping in Extended b‐Metric Spaces With an Application," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    2. Chiming Chen & Ing-Jer Lin, 2013. "Common Fixed Points of Generalized Cyclic Meir‐Keeler‐Type Contractions in Partially Ordered Metric Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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