A common solution of f-fixed point and variational inequality problems in Banach spaces

ABSTRACT

In this paper, we construct a Halpern-type subgradient extragradient iterative algorithm which converges strongly to a common point of the f-fixed point set of a continuous f-pseudocontractive mapping and the solutions set of a variational inequality problem for Lipschitz monotone mapping in reflexive real Banach spaces. In addition, a numerical example is given to demonstrate the behaviour of the convergence of the algorithm. Our results improve, generalize and unify some related recent results in the literature.

KEYWORDS:

• f-fixed point
• f-pseudocontractive mapping
• monotone mapping
• semi-pseudocontractive mapping
• variational inequality

2020 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 47H09
• 47H10
• 47J25
• 47J05
• 47J20

Acknowledgements

The authors express their deep gratitude to the referees and the editor for their valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).