A new class of computationally efficient algorithms for solving fixed-point problems and variational inequalities in real Hilbert spaces

Abstract

Abstract A family of inertial extragradient-type algorithms is proposed for solving convex pseudomonotone variational inequality with fixed-point problems, where the involved mapping for the fixed point is a ρ-demicontractive mapping. Under standard hypotheses, the generated iterative sequence achieves strong convergence to the common solution of the variational inequality and fixed-point problem. Some special cases and sufficient conditions that guarantee the validity of the hypotheses of the convergence statements are also discussed. Numerical applications in detail illustrate the theoretical results and comparison with existing methods.

Keywords

• Fixed-point problem
• ρ-demicontractive mapping
• Variational inequalities
• Strong convergence theorems
• Inertial iterative schemes