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Volume 4, Issue 3, 1 December 2020, Pages 377-398
Abstract. The aim of this paper is to propose two different kinds of self-adaptive algorithms for finding a common solution in the set of solutions of the variational inequality problem with a monotone and Lipschitz continuous operator and the set of fixed points of the mapping satisfying some condition in real Hilbert spaces. The algorithms are combinations of extragradient viscosity-type methods and inertial-type methods. Strong convergence theorems are established without the prior information of the Lipschitz constant of the operator. The proposed algorithms can be regarded as an enhancement of the previously known inertial-type gradient methods in each calculation step. Some numerical examples are also presented.
How to Cite this Article:
Mujahid Abbas, Hira Iqbal, Two Inertial extragradient viscosity algorithms for solving variational inequality and fixed point problems, J. Nonlinear Var. Anal. 4 (2020), 377-398.