A Halpern-type algorithm for a common solution of nonlinear problems in Banach spaces

Abstract

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 f-fixed points of continuous f-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 f-fixed point of continuous f-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.

Keywords

• f-fixed point
• f-pseudocontractive mapping
• monotone mapping
• semi-pseudocontractive mapping
• variational inequality
• strong convergence
• zero points
• 47h05
• 47h10
• 47j25
• 47j05
• 47j20
• 47j26