<p>The primary goal of this paper is to find a common solution of a split variational inclusion problem, a system of variational inequalities problem and common fixed point set of a countable family of nonexpansive mappings in the framework of real Hilbert spaces. Under some suitable conditions imposed on the sequences of parameters, we prove that the sequence induced by the proposed iterative method converges strongly to a common solution of the above stated problems. We derive a consequence from the main convergence result. Further, a numerical example is also provided to demonstrate the efficacy of the proposed iterative method. Finally, a comparison has also been carried out of our algorithm with two existing methods. The technique and conclusions discussed in this paper extend and unify previously published researches in this topic.</p>

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An iterative algorithm for split variational inclusion, a system of variational inequalities and fixed point problems

  • Mubashshir U. Khairoowala,
  • Shamshad Husain,
  • Mohd Furkan

摘要

The primary goal of this paper is to find a common solution of a split variational inclusion problem, a system of variational inequalities problem and common fixed point set of a countable family of nonexpansive mappings in the framework of real Hilbert spaces. Under some suitable conditions imposed on the sequences of parameters, we prove that the sequence induced by the proposed iterative method converges strongly to a common solution of the above stated problems. We derive a consequence from the main convergence result. Further, a numerical example is also provided to demonstrate the efficacy of the proposed iterative method. Finally, a comparison has also been carried out of our algorithm with two existing methods. The technique and conclusions discussed in this paper extend and unify previously published researches in this topic.