Abstract
AbstractIn this paper, we introduce a new mapping in a real Hilbert space to prove a strong convergence theorem for finding a common fixed point of a finite family of strictly pseudo-contractive mappings and a strictly pseudononspreading mapping. Moreover, we also obtain a strong convergence theorem for a finite family of inverse-strongly monotone mappings and a strictly pseudononspreading mapping.
Highlights
1 Introduction In this paper, we assume that H is a real Hilbert space with the inner product ·, · and the induced norm ·, and C is a nonempty closed convex subset of H
A mapping T : C → C is ρ-strictly pseudononspreading if there exists a constant ρ ∈ [, ) such that
Motivated and inspired by the above facts, we define a new mapping for the common fixed point set of a finite family of strict pseudo-contractive mappings
Summary
We assume that H is a real Hilbert space with the inner product ·, · and the induced norm · , and C is a nonempty closed convex subset of H. In , Kangtunyakarn and Suantai [ ] gave the following lemma for the S-mapping generated by T , T , . Kangtunyakarn [ ] proposed an iterative algorithm for finding a common element of the set of fixed points of a κ-strictly pseudononspreading mapping and a finite family of the set of solutions of variational inequality problems as follows. The sequence {xn} converges strongly to z = PFu. Motivated and inspired by the above facts, we define a new mapping for the common fixed point set of a finite family of strict pseudo-contractive mappings. By using our main result, we obtain a new strong convergence theorem for the common fixed point of a finite family of strict pseudo-contractive mappings and a strictly pseudononspreading mapping
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
