Krasnoselski–Mann-type inertial method for solving split generalized mixed equilibrium and hierarchical fixed point problems

In this paper, we present Krasnoselski–Mann-type inertial method for solving split generalized mixed equilibrium and hierarchical fixed point problems for k-strictly pseudocontractive nonself-mappings. We establish that the weak convergence of the proposed accelerated iterative method with inertial terms involves a step size which does not require any prior knowledge of the operator norm under several suitable conditions in Hilbert spaces. Finally, the application to a Nash–Cournot oligopolistic market equilibrium model is discussed, and numerical examples are provided to demonstrate the effectiveness of our iterative method.

Inertial KM-type extragradient scheme for solving a variational inequality and a hierarchical fixed point problems

We propose an inertial KM-type extragradient scheme to approximate a common solution of a variational inequality problem and a hierarchical fixed point problem for nonexpansive mappings. This scheme generalizes and unifies a number of known iterative schemes. Furthermore, we discuss the weak convergence for the proposed scheme. We also discuss an example to illustrate the main theorem.