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

Journal of inequalities and applications

Anchalee Kaewcharoen¹  Preeyanuch Chuasuk² 

[1] Department of Mathematics Faculty of Science, Naresuan University, 65000, Phitsanulok, Thailand;Department of Mathematics, Faculty of Science, Burapha University, 20131, Chonburi, Thailand;

关键词: Hierarchical fixed point problem;    Split generalized mixed equilibrium problem;    Maximal monotonicity;    Nash–Cournot equilibrium model;   

DOI  :  10.1186/s13660-021-02632-9

来源: Springer

【 摘 要 】

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.

【 授权许可】

CC BY