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Solving Split Variational Inclusion Problem and Fixed Point Problem for Nonexpansive Semigroup without Prior Knowledge of Operator Norms

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  • Haitao Che
  • Meixia Li

Abstract

We introduce an iterative method to approximate a common solution of split variational inclusion problem and fixed point problem for nonexpansive semigroups with a way of selecting the stepsizes which does not need any prior information about the operator norms in Hilbert spaces. We prove that the sequences generated by the proposed algorithm converge strongly to a common element of the set of solutions of a split variational inclusion and the set of common fixed points of one-parameter nonexpansive semigroups. Moreover, numerical results demonstrate the performance and convergence of our result, which may be viewed as a refinement and improvement of the previously known results announced by many other researchers.

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  • Haitao Che & Meixia Li, 2015. "Solving Split Variational Inclusion Problem and Fixed Point Problem for Nonexpansive Semigroup without Prior Knowledge of Operator Norms," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-9, November.
    • Handle: RePEc:hin:jnlmpe:408165
    DOI: 10.1155/2015/408165
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    Cited by:

    1. Pawicha Phairatchatniyom & Poom Kumam & Yeol Je Cho & Wachirapong Jirakitpuwapat & Kanokwan Sitthithakerngkiet, 2019. "The Modified Inertial Iterative Algorithm for Solving Split Variational Inclusion Problem for Multi-Valued Quasi Nonexpansive Mappings with Some Applications," Mathematics, MDPI, vol. 7(6), pages 1-22, June.

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