Elijah, Nwakpa Chidi2024-11-072024-11-072024Elijah, Nwakpa Chidi. (2024). Relaxed Inertial Algorithm for Solving Equilibrium Problems [Master’s dissertation, University of the Witwatersrand, Johannesburg]. WireDSpace.https://hdl.handle.net/10539/42246A research report submitted in partial fulfillment of the requirements for the degree of Master of Science to the Faculty of Science, School of Mathematics, University of the Witwatersrand, Johannesburg, 2024In this dissertation, we propose and study two relaxed inertial methods for solving equilibrium problems. In our first proposed method, we establish that the generated sequence of our proposed method weakly converges to a solution of the equilibrium problems. We apply this proposed method to variational inequality and fixed point problems. Further- more, a modification of the first method leads us to our second iterative method. Again, we established that the sequence generated by this method converges strongly to a solution of the equilibrium problems. Our proposed methods involve self-adaptive stepsizes and hence, do not require the fore knowledge of the Lipschitz constants for implementation. In each of our proposed methods, the convergence is established when the associated cost bifunction is pseudomonotone and satisfies the Lipschitz-type conditionen© 2024 University of the Witwatersrand, Johannesburg. All rights reserved. The copyright in this work vests in the University of the Witwatersrand, Johannesburg. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of University of the Witwatersrand, Johannesburg.Relaxed Inertial AlgorithmEquilibriumUCTDSDG-4: Quality educationDissertationUniversity of the Witwatersrand, Johannesburg