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A New Iterative Scheme for Countable Families of Weak Relatively Nonexpansive Mappings and System of Generalized Mixed Equilibrium Problems

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  • Yekini Shehu

Abstract

We construct a new iterative scheme by hybrid methods and prove strong convergence theorem for approximation of a common fixed point of two countable families of weak relatively nonexpansive mappings which is also a solution to a system of generalized mixed equilibrium problems in a uniformly convex real Banach space which is also uniformly smooth using the properties of generalized f‐projection operator. Using this result, we discuss strong convergence theorem concerning general H‐monotone mappings and system of generalized mixed equilibrium problems in Banach spaces. Our results extend many known recent results in the literature.

Suggested Citation

  • Yekini Shehu, 2010. "A New Iterative Scheme for Countable Families of Weak Relatively Nonexpansive Mappings and System of Generalized Mixed Equilibrium Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    • Handle: RePEc:wly:jnlaaa:v:2010:y:2010:i:1:n:861031
    DOI: 10.1155/2010/861031
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    References listed on IDEAS

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    1. Siwaporn Saewan & Poom Kumam & Kriengsak Wattanawitoon, 2010. "Convergence Theorem Based on a New Hybrid Projection Method for Finding a Common Solution of Generalized Equilibrium and Variational Inequality Problems in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-25, January.
    2. Siwaporn Saewan & Poom Kumam, 2010. "Modified Hybrid Block Iterative Algorithm for Convex Feasibility Problems and Generalized Equilibrium Problems for Uniformly Quasi‐ϕ‐Asymptotically Nonexpansive Mappings," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    3. Siwaporn Saewan & Poom Kumam, 2010. "Modified Hybrid Block Iterative Algorithm for Convex Feasibility Problems and Generalized Equilibrium Problems for Uniformly Quasi- -Asymptotically Nonexpansive Mappings," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-22, July.
    4. Siwaporn Saewan & Poom Kumam & Kriengsak Wattanawitoon, 2010. "Convergence Theorem Based on a New Hybrid Projection Method for Finding a Common Solution of Generalized Equilibrium and Variational Inequality Problems in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    5. Siwaporn Saewan & Poom Kumam, 2010. "A Hybrid Iterative Scheme for a Maximal Monotone Operator and Two Countable Families of Relatively Quasi‐Nonexpansive Mappings for Generalized Mixed Equilibrium and Variational Inequality Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
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    Cited by:

    1. Utith Inprasit & Weerayuth Nilsrakoo, 2011. "A Halpern‐Mann Type Iteration for Fixed Point Problems of a Relatively Nonexpansive Mapping and a System of Equilibrium Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    2. Siwaporn Saewan & Poom Kumam, 2011. "Strong Convergence Theorems for Countable Families of Uniformly Quasi‐ϕ‐Asymptotically Nonexpansive Mappings and a System of Generalized Mixed Equilibrium Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).

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