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Strong convergence of an iterative sequence for maximal monotone operators in a Banach space

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  • Fumiaki Kohsaka
  • Wataru Takahashi

Abstract

We first introduce a modified proximal point algorithm for maximal monotone operators in a Banach space. Next, we obtain a strong convergence theorem for resolvents of maximal monotone operators in a Banach space which generalizes the previous result by Kamimura and Takahashi in a Hilbert space. Using this result, we deal with the convex minimization problem and the variational inequality problem in a Banach space.

Suggested Citation

  • Fumiaki Kohsaka & Wataru Takahashi, 2004. "Strong convergence of an iterative sequence for maximal monotone operators in a Banach space," Abstract and Applied Analysis, Hindawi, vol. 2004, pages 1-11, January.
    • Handle: RePEc:hin:jnlaaa:240462
    DOI: 10.1155/S1085337504309036
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    Cited by:

    1. Pongrus Phuangphoo & Poom Kumam, 2013. "A New Hybrid Projection Algorithm for System of Equilibrium Problems and Variational Inequality Problems and Two Finite Families of Quasi‐ϕ‐Nonexpansive Mappings," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Yaqin Wang, 2012. "A New Hybrid Method for Equilibrium Problems, Variational Inequality Problems, Fixed Point Problems, and Zero of Maximal Monotone Operators," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. Prasit Cholamjiak & Suthep Suantai & Yeol Je Cho, 2012. "Strong Convergence to Solutions of Generalized Mixed Equilibrium Problems with Applications," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    4. Kriengsak Wattanawitoon & Poom Kumam, 2012. "A New Iterative Scheme for Generalized Mixed Equilibrium, Variational Inequality Problems, and a Zero Point of Maximal Monotone Operators," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    5. Ali Abkar & Elahe Shahrosvand & Azizollah Azizi, 2017. "The Split Common Fixed Point Problem for a Family of Multivalued Quasinonexpansive Mappings and Totally Asymptotically Strictly Pseudocontractive Mappings in Banach Spaces," Mathematics, MDPI, vol. 5(1), pages 1-18, February.
    6. Jingling Zhang & Yongfu Su & Qingqing Cheng, 2012. "Hybrid Algorithm of Fixed Point for Weak Relatively Nonexpansive Multivalued Mappings and Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    7. Kasamsuk Ungchittrakool, 2013. "Existence and Convergence Theorems by an Iterative Shrinking Projection Method of a Strict Pseudocontraction in Hilbert Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    8. Chakkrid Klin-eam & Suthep Suantai & Wataru Takahashi, 2009. "Strong Convergence of Generalized Projection Algorithms for Nonlinear Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    9. Mathew O. Aibinu & Surendra C. Thakur & Sibusiso Moyo, 2020. "Algorithm for Solutions of Nonlinear Equations of Strongly Monotone Type and Applications to Convex Minimization and Variational Inequality Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2020(1).
    10. 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).
    11. Somyot Plubtieng & Wanna Sriprad, 2009. "Strong and Weak Convergence of Modified Mann Iteration for New Resolvents of Maximal Monotone Operators in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    12. 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).

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