Nonlinear Functional Analysis and Applications

The Basic Sciences Research Institute, Kyungnam University (경남대학교 기초과학연구소)
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IMPROVED GENERALIZED M-ITERATION FOR QUASI-NONEXPANSIVE MULTIVALUED MAPPINGS WITH APPLICATION IN REAL HILBERT SPACES

  • Akutsah, Francis (School of Mathematics, Statistics and Computer Science University of KwaZulu-Natal) ;
  • Narain, Ojen Kumar (School of Mathematics, Statistics and Computer Science University of KwaZulu-Natal) ;
  • Kim, Jong Kyu (Department of Mathematics Education Kyungnam University)
  • Received : 2021.04.05
  • Accepted : 2021.09.11
  • Published : 2022.03.15
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Abstract

In this paper, we present a modified (improved) generalized M-iteration with the inertial technique for three quasi-nonexpansive multivalued mappings in a real Hilbert space. In addition, we obtain a weak convergence result under suitable conditions and the strong convergence result is achieved using the hybrid projection method with our modified generalized M-iteration. Finally, we apply our convergence results to certain optimization problem, and present some numerical experiments to show the efficiency and applicability of the proposed method in comparison with other improved iterative methods (modified SP-iterative scheme) in the literature. The results obtained in this paper extend, generalize and improve several results in this direction.

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References

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