On the split common fixed point problem for strict pseudocontractive and asymptotically nonexpansive mappings in Banach spaces

Jinfang Tang,Shih-Sen Chang,Xiongrui Wang,Lin Wang

doi:10.1186/s13660-015-0832-z

Abstract

In this paper, we prove a weak convergence theorem and a strong convergence theorem for split common fixed point problem involving a quasi-strict pseudo contractive mapping and an asymptotical nonexpansive mapping in the setting of two Banach spaces. Our results are new and seem to be the first outside Hilbert spaces.

Highlights

Let H and H be two real Hilbert spaces, C and Q be nonempty closed convex subsets of H and H, respectively, and A : H → H be a bounded linear operator
We use to denote the set of solutions of split common fixed point problem (SCFP) for mappings S and T, that is
( ) E is a real Banach space. ( ) A : E → E is a bounded linear operator and A∗ is the adjoint of A. ( ) S : E → E is an {ln}-asymptotical nonexpansive mapping with {ln} ⊂ (, ∞) and ln →

Summary

Introduction

Let H and H be two real Hilbert spaces, C and Q be nonempty closed convex subsets of H and H , respectively, and A : H → H be a bounded linear operator. In , Cui and Wang [ ] investigated the split common fixed point problems of τ -quasi-strict pseudocontractive mappings in the setting of two Hilbert spaces.

Results

Conclusion