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An Inertial Type Algorithm for Extended Split Equality Variational Inclusion and Fixed Point Problems

Abstract

In this article, we study an extended split equality variational inclusion and fixed point problems which is an extension of the split equality variational inclusion problems and fixed point problems. We propose a simultaneous inertial type iterative algorithm with a self adaptive stepsizes such that there is no need for a prior information about the operator norm. We further stated and prove that the proposed algorithm weakly converges to a solution of the extended split equality variational inclusion and fixed point problems. Finally, we give some numerical examples to demonstrate the performance and the applicability of the proposed algorithm. The results of this paper complements and extends results on split equality variational inclusion and fixed point problems.

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Acknowledgements

This work is based on the research supported wholly by the National Research Foundation (NRF) of South Africa (Grant number 111992). Opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to the NRF.

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Correspondence to Ferdinard Udochukwu Ogbuisi.

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Communicated by Behzad Djafari-Rouhani.

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Ogbuisi, F.U. An Inertial Type Algorithm for Extended Split Equality Variational Inclusion and Fixed Point Problems. Bull. Iran. Math. Soc. (2021). https://doi.org/10.1007/s41980-021-00634-3

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Keywords

  • Inertial term
  • Maximal monotone mapping
  • Resolvent
  • Extended spit equality variational inclusion problem
  • Fixed point problem

Mathematics Subject Classification

  • 47H05
  • 47H06
  • 47H30
  • 47J05
  • 47J25