Modified Inertial Hybrid and Shrinking Projection Algorithms for Solving Fixed Point Problems

Abstract

In this paper, we introduce two modified inertial hybrid and shrinking projection algorithms for solving fixed point problems by combining the modified inertial Mann algorithm with the projection algorithm. We establish strong convergence theorems under certain suitable conditions. Finally, our algorithms are applied to convex feasibility problem, variational inequality problem, and location theory. The algorithms and results presented in this paper can summarize and unify corresponding results previously known in this field.

Keywords

• conjugate gradient method
• steepest descent method
• hybrid projection
• shrinking projection
• inertial mann
• strongly convergence
• nonexpansive mapping