Hybrid Steepest Descent Method for Solving the Split Fixed Point Problem in Banach Spaces

Ali Abkar, Elahe Shahrosvand

Abstract

In this paper we introduce two algorithms based on the hybrid steepest descent method which converge to a solution of the split fixed point problem for $\lambda$-strictly pseudo-contractive mappings in uniformly convex and 2-uniformly smooth Banach spaces. Our results improve and extend the results of Q. H. Ansari et al. (2016), Y. Yao et al. (2013), and those of J. S. Jung (2016).

In this paper we introduce two
algorithms based on the hybrid steepest descent method which converge to a solution of
the split fixed point problem for $\lambda$-strictly pseudo-contractive
mappings in uniformly convex and 2-uniformly smooth Banach spaces.
Our results improve and extend the results of Ansari et al \cite{Ansari}, Yao et al \cite{Yao} and
Jung \cite{Jung}.In this paper we introduce two
algorithms based on the hybrid steepest descent method which converge to a solution of
the split fixed point problem for $\lambda$-strictly pseudo-contractive
mappings in uniformly convex and 2-uniformly smooth Banach spaces.
Our results improve and extend the results of Ansari et al \cite{Ansari}, Yao et al \cite{Yao} and
Jung \cite{Jung}.