Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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INERTIAL PROXIMAL AND CONTRACTION METHODS FOR SOLVING MONOTONE VARIATIONAL INCLUSION AND FIXED POINT PROBLEMS

  • Jacob Ashiwere Abuchu (School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Department of Mathematics, University of Calabar) ;
  • Godwin Chidi Ugwunnadi (Department of Mathematics, University of Eswatini, Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University) ;
  • Ojen Kumar Narain (School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal)
  • Received : 2022.03.26
  • Accepted : 2022.09.17
  • Published : 2023.03.03
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Abstract

In this paper, we study an iterative algorithm that is based on inertial proximal and contraction methods embellished with relaxation technique, for finding common solution of monotone variational inclusion, and fixed point problems of pseudocontractive mapping in real Hilbert spaces. We establish a strong convergence result of the proposed iterative method based on prediction stepsize conditions, and under some standard assumptions on the algorithm parameters. Finally, some special cases of general problem are given as applications. Our results improve and generalized some well-known and related results in literature.

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Acknowledgement

The authors sincerely appreciate the anonymous referees and the handling Editor for their constructive comments and fruitful suggestions which have immensely improved the earlier version of the manuscript.

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