The Split Equality Fixed Point Problem for Quasi-Pseudo-Contractive Mappings Without Prior Knowledge of Norms

Abstract

Recently, Chang et al. (2015) constructed an algorithm that converges weakly to the solution of the split equality fixed point problem for quasi-pseudo-contractive mappings under some suitable conditions. They also showed that strong convergence is obtained in the case when the quasi-pseudo-contractive mappings are semi-compact. In this article, we construct an algorithm for quasi-pseudo-contractive mappings that always converge strongly to some solution of the split equality fixed point problem under mild conditions. We mention that we do not require the quasi-pseudo-contractive mappings to be semi-compact to obtain strong convergence. The algorithm does not require any prior knowledge of operator norms. The result of this article provides a unified framework for this type of problems.

Keywords:

• Demicontractive operators
• directed operators
• fixed point
• feasibility problem
• quasi nonexpansive mapping
• quasi-pseudo contractive mapping

MATHEMATICS SUBJECT CLASSIFICATION:

• 47H09
• 47H10
• 47H20
• 47J20
• 65J15