Volume 46_4(2025)_247-291

Introduction to Halpern-type strong convergence theorems to solve fixed point problems

Atsumasa Kondo 

Abstract. This study addresses strong convergence theorems for finding fixed points and com- mon fixed points of nonlinear mappings using Halpern-type iterative methods. By arranging some significant theorems in an order that is logically easy to understand the proofs, this article guides students or people outside the field through Halpern-type strong convergence theorems with rigorous proofs. After reading this article, the readers can easily understand some of well- known original research articles. An application to a common variational inequality problem is also presented as an application.

Rend. Mat. Appl. (7) 46 (2025) 247-291; pdf