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Authors: OLAWALE K. OYEWOLE, AKINDELE A. MEBAWONDU, OLUWATOSIN T. MEWOMO.
Received 21 May 2021; Accepted 14 July 2021. Published Online: 2024-03-20
Published Print: 2024-03-30
pp. 183-209
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In this paper, we propose an iterative algorithm for approximating a common solution of a variational inequality and fixed point problem. The algorithm combines the subgradient extragradient technique, inertial method and a modified viscosity approach. Using this algorithm, we state and prove a strong convergence algorithm for obtaining a common solution of a pseudomonotone variational inequality problem and fixed point of an η-demimetric mapping in a real Hilbert space. We give an application of this result to some theoretical optimization problems. Furthermore, we report some numerical examples to show the efficiency of our method by comparing with previous methods in the literature. Our result extend, improve and unify many other results in this direction in the literature.
Mathematics Subject Classification (2010): 47H09, 49J35, 90C47.
Keywords: Variational inequality, pseudomonotone operator, strong convergence, fixed point, extragradient algorithm, linesearch rule, Hilbert space.
