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Two block hybrid projection method for solving a common solution for a system of generalized equilibrium problems and fixed point problems for two countable families

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Abstract

In this paper, we introduce a new iterative sequence which is constructed by using the new modified two block hybrid projection method for solving the common solution problem for a system of generalized equilibrium problems of inverse strongly monotone mappings and a system of bifunctions satisfying certain conditions, and the common fixed point problems for families of uniformly quasi -\({\phi}\) - asymptotically nonexpansive and locally uniformly Lipschitz continuous. Strong convergence theorems are proved on approximating a common solution of a system of generalized equilibrium problems and fixed point problems for two countable families in Banach spaces. Our results presented in this paper improve and extend many recent results in this area.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangmod, Thungkru, Bangkok, 10140, Thailand

    Pongrus Phuangphoo & Poom Kumam

  2. Computational Science and Engineering Research Cluster (CSEC), King Mongkut’s University of Technology Thonburi (KMUTT), Bangmod, Thrungkru, Bangkok, 10140, Thailand

    Poom Kumam

Authors
  1. Pongrus Phuangphoo
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  2. Poom Kumam
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Correspondence to Poom Kumam.

Additional information

This work was supported by the Higher Education Research Promotion and the National Research University Project of Thailand, Office of the Higher Education Commission (under NRU55-CSEC Project No. 55000613).

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Phuangphoo, P., Kumam, P. Two block hybrid projection method for solving a common solution for a system of generalized equilibrium problems and fixed point problems for two countable families. Optim Lett 7, 1745–1763 (2013). https://doi.org/10.1007/s11590-012-0520-6

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  • DOI: https://doi.org/10.1007/s11590-012-0520-6

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