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Invariant Approximation Results via Common Fixed Point Theorems for Generalized Weak Contraction Maps

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  • Savita Rathee
  • Anil Kumar
  • Kenan Tas

Abstract

A common fixed point theorem for generalized (φ, ϕ, L )f,g‐weak contraction in a metric space is established. As an application, some common fixed point results in normed linear spaces are obtained. We also study some results on best approximation via common fixed point theorems. Our result improves some results from the existing literature. Some illustrative examples to highlight the realized improvements are also furnished.

Suggested Citation

  • Savita Rathee & Anil Kumar & Kenan Tas, 2014. "Invariant Approximation Results via Common Fixed Point Theorems for Generalized Weak Contraction Maps," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:752107
    DOI: 10.1155/2014/752107
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    References listed on IDEAS

    as
    1. Anil Kumar & Savita Rathee & Navin Kumar, 2013. "The Point of Coincidence and Common Fixed Point for Three Mappings in Cone Metric Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    2. Anil Kumar & Savita Rathee & Navin Kumar, 2013. "The Point of Coincidence and Common Fixed Point for Three Mappings in Cone Metric Spaces," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-6, June.
    3. Mohamed Jleli & Erdal Karapınar & Bessem Samet, 2012. "Fixed Point Results for Almost Generalized Cyclic (ψ, φ)‐Weak Contractive Type Mappings with Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. Gerald Jungck, 1986. "Compatible mappings and common fixed points," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 9, pages 1-9, January.
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