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

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  • Kasamsuk Ungchittrakool
  • Duangkamon Kumtaeng

Abstract

We create some new ideas of mappings called quasi-strict -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 -projection, we propose an iterative shrinking metric -projection method for finding a common fixed point of a quasi-strict -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 -Projection Method for Finding a Common Fixed Point of a Closed and Quasi-Strict -Pseudocontraction and a Countable Family of Firmly Nonexpansive Mappings and Application," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, December.
    • Handle: RePEc:hin:jnlaaa:589282
    DOI: 10.1155/2013/589282
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