Solvability of a class of set-valued implicit quasi-variational inequalities: A Wiener–Hopf equation method

Abstract

In this paper, we consider a class of set-valued implicit quasi-variational inequalities in real Banach spaces and show its equivalence with a class of fixed point equations and a class of Wiener–Hopf equations. Using these equivalences, we propose and analyze some iterative algorithms for this class of variational inequalities. Further, we give existence of solution and discuss the convergence criteria of the sequences generated by the iterative algorithms for this class of set-valued implicit quasi-variational inequalities. The results presented in this paper generalize and unify many known results in the literature.

Keywords

• Set-valued implicit quasi-variational inequalities
• Retraction mapping
• Ishikawa iterative algorithm
• Implicit Wiener–Hopf equations
• Convergence analysis