An algorithm for approximating a common solution of some nonlinear problems in Banach spaces with an application. (English) Zbl 1502.47080
Summary: 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.
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 47J20 | Variational and other types of inequalities involving nonlinear operators (general) |
Keywords:
Halpern-type subgradient extragradient iterative algorithm; strong convergence; pseudo-contractive maps; fixed points; variational inequality; equilibrium problems; uniformly smooth Banach spaceReferences:
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