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Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces

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  • Dan Butnariu
  • Elena Resmerita

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  • Dan Butnariu & Elena Resmerita, 2006. "Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2006(1).
    • Handle: RePEc:wly:jnlaaa:v:2006:y:2006:i:1:n:084919
    DOI: 10.1155/AAA/2006/84919
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    References listed on IDEAS

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    1. Takanori Ibaraki & Yasunori Kimura & Wataru Takahashi, 2003. "Convergence theorems for generalized projections and maximal monotone operators in Banach spaces," Abstract and Applied Analysis, Hindawi, vol. 2003, pages 1-9, January.
    2. Takanori Ibaraki & Yasunori Kimura & Wataru Takahashi, 2003. "Convergence theorems for generalized projections and maximal monotone operators in Banach spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2003(10), pages 621-629.
    3. Jonathan Eckstein, 1993. "Nonlinear Proximal Point Algorithms Using Bregman Functions, with Applications to Convex Programming," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 202-226, February.
    4. Y. Alber & D. Butnariu, 1997. "Convergence of Bregman Projection Methods for Solving Consistent Convex Feasibility Problems in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 92(1), pages 33-61, January.
    5. M. V. Solodov & B. F. Svaiter, 2000. "An Inexact Hybrid Generalized Proximal Point Algorithm and Some New Results on the Theory of Bregman Functions," Mathematics of Operations Research, INFORMS, vol. 25(2), pages 214-230, May.
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    Cited by:

    1. M. De la Sen, 2013. "On Best Proximity Point Theorems and Fixed Point Theorems for p‐Cyclic Hybrid Self‐Mappings in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Hiroko Manaka, 2015. "Fixed Point Theorems for an Elastic Nonlinear Mapping in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).
    3. Mohammed Ali Alghamdi & Naseer Shahzad & Habtu Zegeye, 2014. "Strong Convergence Theorems for Quasi‐Bregman Nonexpansive Mappings in Reflexive Banach Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    4. Hiroko Manaka, 2010. "Convergence Theorems for a Maximal Monotone Operator and a V‐Strongly Nonexpansive Mapping in a Banach Space," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    5. Li-Wei Kuo & D. R. Sahu, 2013. "Bregman Distance and Strong Convergence of Proximal‐Type Algorithms," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    6. Eskandar Naraghirad & Ngai-Ching Wong & Jen-Chih Yao, 2014. "Applications of Bregman‐Opial Property to Bregman Nonspreading Mappings in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    7. Chin-Tzong Pang & Eskandar Naraghirad, 2013. "Bregman Asymptotic Pointwise Nonexpansive Mappings in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    8. Nguyen Trung Hieu & Nguyen Dung, 2025. "An inertial parallel iterative method for solving generalized mixed equilibrium problems and common fixed point problem in reflexive Banach spaces," Indian Journal of Pure and Applied Mathematics, Springer, vol. 56(4), pages 1398-1415, December.
    9. Chin-Tzong Pang & Eskandar Naraghirad & Ching-Feng Wen, 2014. "Bregman f‐Projection Operator with Applications to Variational Inequalities in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    10. Shenghua Wang & Shin Min Kang, 2013. "Strong Convergence Iterative Algorithms for Equilibrium Problems and Fixed Point Problems in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    11. H. Zegeye & N. Shahzad, 2014. "Convergence Theorems for Right Bregman Strongly Nonexpansive Mappings in Reflexive Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    12. Chin-Tzong Pang & Eskandar Naraghirad & Ching-Feng Wen, 2014. "Weak Convergence Theorems for Bregman Relatively Nonexpansive Mappings in Banach Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    13. Jinhua Zhu & Shih-sen Chang & Min Liu, 2013. "Strong Convergence Theorem for Bregman Strongly Nonexpansive Mappings and Equilibrium Problems in Reflexive Banach Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    14. Thomas Bonesky & Kamil S. Kazimierski & Peter Maass & Frank Schöpfer & Thomas Schuster, 2008. "Minimization of Tikhonov Functionals in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2008(1).

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