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Strong convergence theorem for a system of generalized mixed equilibrium problems and finite family of Bregman nonexpansive mappings in Banach spaces

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  • Vahid Darvish

    (Amirkabir University of Technology)

Abstract

In this paper we introduce a general iterative algorithm for finding the common element of the set of common fixed points of a finite family of Bregman nonexpansive mappings and the set of solutions of systems of generalized mixed equilibrium problems. As an application, we find a solution for system of mixed variational inequality.

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  • Vahid Darvish, 2016. "Strong convergence theorem for a system of generalized mixed equilibrium problems and finite family of Bregman nonexpansive mappings in Banach spaces," OPSEARCH, Springer;Operational Research Society of India, vol. 53(3), pages 584-603, September.
    • Handle: RePEc:spr:opsear:v:53:y:2016:i:3:d:10.1007_s12597-015-0245-2
    DOI: 10.1007/s12597-015-0245-2
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    References listed on IDEAS

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    1. W. Takahashi & M. Toyoda, 2003. "Weak Convergence Theorems for Nonexpansive Mappings and Monotone Mappings," Journal of Optimization Theory and Applications, Springer, vol. 118(2), pages 417-428, August.
    2. H.K. Xu, 2003. "An Iterative Approach to Quadratic Optimization," Journal of Optimization Theory and Applications, Springer, vol. 116(3), pages 659-678, March.
    3. Simeon Reich & Shoham Sabach, 2011. "Existence and Approximation of Fixed Points of Bregman Firmly Nonexpansive Mappings in Reflexive Banach Spaces," Springer Optimization and Its Applications, in: Heinz H. Bauschke & Regina S. Burachik & Patrick L. Combettes & Veit Elser & D. Russell Luke & Henry (ed.), Fixed-Point Algorithms for Inverse Problems in Science and Engineering, chapter 0, pages 301-316, Springer.
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