A Halpern-type algorithm for a common solution of nonlinear problems in Banach spaces - Zegeye, Habtu; Boikanyo, Oganeditse A. (Topological algebra and its applications, 2023)
In this article, we propose a Halpern-type subgradient extragradient algorithm for solving a common element of the set of solutions of variational inequality problems for continuous monotone mappings and the set of -fixed points of continuous -pseudocontractive mappings in reflexive real Banach spaces. In addition, we prove a strong convergence theorem for the sequence generated by the algorithm. As a consequence, we obtain a scheme that converges strongly to a common -fixed point of continuous -pseudocontractive mappings and a scheme that converges strongly to a common zero of continuous monotone mappings in Banach spaces. Furthermore, we provide a numerical example to illustrate the implementability of our algorithm.