An algorithm for approximating a common solution of some nonlinear problems in Banach spaces with an application

Abstract

In this paper, we construct a new Halpern-type subgradient extragradient iterative algorithm. The sequence generated by this algorithm converges strongly to a common solution of a variational inequality, an equilibrium problem, and a J-fixed point of a continuous J-pseudo-contractive map in a uniformly smooth and two-uniformly convex real Banach space. Also, the theorem is applied to approximate a common solution of a variational inequality, an equilibrium problem, and a convex minimization problem. Moreover, a numerical example is given to illustrate the implementability of our algorithm. Finally, the theorem proved complements, improves, and unifies some related recent results in the literature.