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A New General System of Generalized Nonlinear Mixed Composite‐Type Equilibria and Fixed Point Problems with an Application to Minimization Problems

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  • Pongsakorn Sunthrayuth
  • Poom Kumam

Abstract

We introduce a new general system of generalized nonlinear mixed composite‐type equilibria and propose a new iterative scheme for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a general system of generalized nonlinear mixed composite‐type equilibria, and the set of fixed points of a countable family of strict pseudocontraction mappings. Furthermore, we prove the strong convergence theorem of the purposed iterative scheme in a real Hilbert space. As applications, we apply our results to solve a certain minimization problem related to a strongly positive bounded linear operator. Finally, we also give a numerical example which supports our results. The results obtained in this paper extend the recent ones announced by many others.

Suggested Citation

  • Pongsakorn Sunthrayuth & Poom Kumam, 2012. "A New General System of Generalized Nonlinear Mixed Composite‐Type Equilibria and Fixed Point Problems with an Application to Minimization Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:414718
    DOI: 10.1155/2012/414718
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    1. Pongsakorn Sunthrayuth & Poom Kumam, 2012. "A System of Generalized Mixed Equilibrium Problems, Maximal Monotone Operators, and Fixed Point Problems with Application to Optimization Problems," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-39, December.
    2. Pongsakorn Sunthrayuth & Poom Kumam, 2012. "A System of Generalized Mixed Equilibrium Problems, Maximal Monotone Operators, and Fixed Point Problems with Application to Optimization Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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