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An Iterative Shrinking Metric f‐Projection Method for Finding a Common Fixed Point of a Closed and Quasi‐Strictf‐Pseudocontraction and a Countable Family of Firmly Nonexpansive Mappings and Applications in Hilbert Spaces

Author

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  • Kasamsuk Ungchittrakool
  • Duangkamon Kumtaeng

Abstract

We create some new ideas of mappings called quasi‐strict f‐pseudocontractions. Moreover, we also find the significant inequality related to such mappings and firmly nonexpansive mappings within the framework of Hilbert spaces. By using the ideas of metric f‐projection, we propose an iterative shrinking metric f‐projection method for finding a common fixed point of a quasi‐strict f‐pseudocontraction and a countable family of firmly nonexpansive mappings. In addition, we provide some applications of the main theorem to find a common solution of fixed point problems and generalized mixed equilibrium problems as well as other related results.

Suggested Citation

  • Kasamsuk Ungchittrakool & Duangkamon Kumtaeng, 2013. "An Iterative Shrinking Metric f‐Projection Method for Finding a Common Fixed Point of a Closed and Quasi‐Strictf‐Pseudocontraction and a Countable Family of Firmly Nonexpansive Mappings and Applications in Hilbert Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:589282
    DOI: 10.1155/2013/589282
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    References listed on IDEAS

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    1. Heinz H. Bauschke & Patrick L. Combettes, 2001. "A Weak-to-Strong Convergence Principle for Fejér-Monotone Methods in Hilbert Spaces," Mathematics of Operations Research, INFORMS, vol. 26(2), pages 248-264, May.
    2. Klaus Deimling, 1985. "Nonlinear Functional Analysis," Springer Books, Springer, number 978-3-662-00547-7, October.
    3. Kasamsuk Ungchittrakool, 2010. "A Strong Convergence Theorem for a Common Fixed Point of Two Sequences of Strictly Pseudocontractive Mappings in Hilbert Spaces and Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    4. Kasamsuk Ungchittrakool, 2010. "A Strong Convergence Theorem for a Common Fixed Point of Two Sequences of Strictly Pseudocontractive Mappings in Hilbert Spaces and Applications," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-17, December.
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