Nonlinear Functional Analysis and Applications

The Basic Sciences Research Institute, Kyungnam University (경남대학교 기초과학연구소)
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SOLVING QUASIMONOTONE SPLIT VARIATIONAL INEQUALITY PROBLEM AND FIXED POINT PROBLEM IN HILBERT SPACES

  • D. O. Peter (School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal) ;
  • A. A. Mebawondu (School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal) ;
  • G. C. Ugwunnadi (Department of Mathematics, University of Eswatini) ;
  • P. Pillay (School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal) ;
  • O. K. Narain (School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal)
  • Received : 2022.05.10
  • Accepted : 2022.07.04
  • Published : 2023.03.03
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Abstract

In this paper, we introduce and study an iterative technique for solving quasimonotone split variational inequality problems and fixed point problem in the framework of real Hilbert spaces. Our proposed iterative technique is self adaptive, and easy to implement. We establish that the proposed iterative technique converges strongly to a minimum-norm solution of the problem and give some numerical illustrations in comparison with other methods in the literature to support our strong convergence result.

Keywords

Acknowledgement

The second author acknowledges with thanks the bursary and financial support from Department of Science and Technology and National Research Foundation, Republic of South Africa Centre of Excellence in Mathematical and Statistical Sciences (DST-NRF CoE-MaSS) Postdoctoral Fellowship. Opinions stated and conclusions reached are solely those of the author and should not be ascribed to the CoE-MaSS in any way.

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