An algorithm for approximating a common solution of variational inequality and convex minimization problems

LetXbe a uniformly smooth and 2-uniformly convex real Banach space with dual space. In this paper, a Halpern-type subgradient extragradient algorithm is constructed. The sequence, generated by the algorithm, converges strongly to a common solution of variational inequality and two convex minimization problems. This result is obtained as an application of a Halpern-type subgradient extragradient algorithm, for approximating a common solution of variational inequality andJ-fixed points of two continuousJ-pseudocontractions. The theorem proved complements, improves and unifies many recent results in the literature. Finally, numerical experiments are given to illustrate the convergence of the sequence generated by the algorithm.