A New Construction and Convergence Analysis of Non-Monotonic Iterative Methods for Solving ρ-Demicontractive Fixed Point Problems and Variational Inequalities Involving Pseudomonotone Mapping
Abstract:Two new inertial-type extragradient methods are proposed to find a numerical common solution to the variational inequality problem involving a pseudomonotone and Lipschitz continuous operator, as well as the fixed point problem in real Hilbert spaces with a ρ-demicontractive mapping. These inertial-type iterative methods use self-adaptive step size rules that do not require previous knowledge of the Lipschitz constant. We also show that the proposed methods strongly converge to a solution of the variational in… Show more
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