Nonlinear Functional Analysis and Applications

The Basic Sciences Research Institute, Kyungnam University (경남대학교 기초과학연구소)
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A NEW RELAXED TSENG METHOD FOR FINDING A COMMON SOLUTION OF FIXED POINT AND SPLIT MONOTONE INCLUSION PROBLEMS

  • Lusanda Mzimela (School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal) ;
  • Akindele Adebayo Mebawondu (Department of Computer Science and Mathematics, Mountain Top University, School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal) ;
  • Adhir Maharaj (Department of Mathematics, Durban University of Technology) ;
  • Chinedu Izuchukwu (School of Mathematics, University of the Witwatersrand) ;
  • Ojen Kumar Narain (School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal)
  • Received : 2023.08.01
  • Accepted : 2023.09.08
  • Published : 2024.03.15
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Abstract

In this paper, we study the problem of finding a common solution to a fixed point problem involving a finite family of ρ-demimetric operators and a split monotone inclusion problem with monotone and Lipschitz continuous operator in real Hilbert spaces. Motivated by the inertial technique and the Tseng method, a new and efficient iterative method for solving the aforementioned problem is introduced and studied. Also, we establish a strong convergence result of the proposed method under standard and mild conditions.

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References

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