A self adaptive inertial subgradient extragradient algorithm for variational inequality and common fixed point of multivalued mappings in Hilbert spaces

Abstract

We consider a new subgradient extragradient iterative algorithm with inertial extrapolation for approximating a common solution of variational inequality problems and fixed point problems of a multivalued demicontractive mapping in a real Hilbert space. We established a strong convergence theorem for our proposed algorithm under some suitable conditions and without prior knowledge of the Lipschitz constant of the underlying operator. We present numerical examples to show that our proposed algorithm performs better than some recent existing algorithms in the literature.

Keywords

• variational inequality
• extragradient method
• fixed point problem
• accelerated algorithm
• demicontractive mappings
• viscosity approximation method
• 49j40
• 58e35
• 65k15
• 90c33