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Inertial-Viscosity-Type Algorithms for Solving Generalized Equilibrium and Fixed Point Problems in Hilbert Spaces

Abstract

In this paper, we introduce a new algorithm of inertial form for solving Split Generalized Equilibrium Problem (SGEP) and Fixed Point Problem (FPP) of multivalued nonexpansive mappings in real Hilbert spaces. Motivated by the viscosity-type method, we incorporate the inertial technique to accelerate the convergence of the proposed method. Here, the viscosity term is a function of the inertial extrapolation sequence and some assumptions on the bifunctions are dispensed with. Under standard and mild assumption of monotonicity and upper hemicontinuity of the SGEP associated mappings, we establish the strong convergence of the scheme which also solves a Variational Inequality Problem (VIP). A numerical example is presented to illustrate the effectiveness and performance of our method as well as comparing it with a related method and conventional inertial-viscosity-type algorithm in the literature.

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Acknowledgements

The first author acknowledges with thanks the International Mathematical Union Breakout Graduate Fellowship (IMU-BGF) Award for his doctoral study. The second author is supported by the National Research Foundation (NRF) of South Africa Incentive Funding for Rated Researchers (Grant Number 119903). Opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to the IMU and NRF.

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Correspondence to Oluwatosin Temitope Mewomo.

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Taiwo, A., Mewomo, O.T. Inertial-Viscosity-Type Algorithms for Solving Generalized Equilibrium and Fixed Point Problems in Hilbert Spaces. Vietnam J. Math. 50, 125–149 (2022). https://doi.org/10.1007/s10013-021-00485-9

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  • DOI: https://doi.org/10.1007/s10013-021-00485-9

Keywords

  • Fixed point problem
  • Generalized equilibrium problem
  • Multivalued non-expansive mapping
  • Hilbert spaces

Mathematics Subject Classification (2010)

  • 47H10
  • 47J22
  • 47J25
  • 65J15