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Strong convergence of an iterative method for solving the multiple-set split equality fixed point problem in a real Hilbert space

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this paper we consider the problem of minimizing a non necessarily differentiable convex function over the intersection of fixed point sets associated with an infinite family of multivalued quasi-nonexpansive mappings in a real Hilbert space. The new algorithm allows us to solve problems when the mappings are not necessarily projection operators or when the computation of projections is not an easy task. The a priori knowledge of operator norms is avoided and conditions to get the strong convergence of the new algorithm are given. Finally the particular case of split equality fixed point problems for family of multivalued mappings is displayed. Our general algorithm can be considered as an extension of Shehu’s method to a larger class of problems.

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Authors and Affiliations

  1. Institute for Computational Science and Technology at Ho Chi Minh City (ICST), Ho Chi Minh City, Vietnam

    Dinh Minh Giang, Jean Jacques Strodiot & Van Hien Nguyen

  2. University of Namur, Namur, Belgium

    Jean Jacques Strodiot & Van Hien Nguyen

Authors
  1. Dinh Minh Giang
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  2. Jean Jacques Strodiot
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  3. Van Hien Nguyen
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Corresponding author

Correspondence to Jean Jacques Strodiot.

Additional information

The authors would like to thank the referee and the Associate Editor for their valuable comments. This research is funded by the Department of Science and Technology at Ho Chi Minh City, Vietnam. Support provided by the Institute for Computational Science and Technology (ICST) at Ho Chi Minh City is gratefully acknowledged.

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Giang, D.M., Strodiot, J.J. & Nguyen, V.H. Strong convergence of an iterative method for solving the multiple-set split equality fixed point problem in a real Hilbert space. RACSAM 111, 983–998 (2017). https://doi.org/10.1007/s13398-016-0338-7

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  • DOI: https://doi.org/10.1007/s13398-016-0338-7

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