Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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AN INERTIAL TSENG ALGORITHM FOR SOLVING QUASIMONOTONE VARIATIONAL INEQUALITY AND FIXED POINT PROBLEM IN HILBERT SPACES

  • Shamsudeen Abiodun Kajola (School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal) ;
  • Ojen Kumar Narain (School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal) ;
  • Adhir Maharaj (Department of Mathematics, Durban University of Technology)
  • Received : 2023.11.16
  • Accepted : 2024.03.19
  • Published : 2024.09.15
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Abstract

In this paper, we propose an inertial method for solving a common solution to fixed point and Variational Inequality Problem in Hilbert spaces. Under some standard and suitable assumptions on the control parameters, we prove that the sequence generated by the proposed algorithm converges strongly to an element in the solution set of Variational Inequality Problem associated with a quasimonotone operator which is also solution to a fixed point problem for a demimetric mapping. Finally, we give some numerical experiments for supporting our main results and also compare with some earlier announced methods in the literature.

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References

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