Abstract
Let H be a real Hilbert space, K a nonempty subset of H, and $T:K\rightarrow \mathit{CB}(K)$ a multi-valued mapping. Then T is called a generalized k-strictly pseudo-contractive multi-valued mapping if there exists $k\in[0,1)$ such that, for all $x,y\in D(T)$ , we have $D^{2}(Tx,Ty)\leq\|x-y\|^{2}+kD^{2}(Ax,Ay)$ , where $A:=I-T$ , and I is the identity operator on K. A Krasnoselskii-type algorithm is constructed and proved to be an approximate fixed point sequence for a common fixed point of a finite family of this class of maps. Furthermore, assuming existence, strong convergence to a common fixed point of the family is proved under appropriate additional assumptions.
Highlights
Let H be a real Hilbert space, CB(H) denote the collection of nonempty, closed, and bounded subsets of H
The fixed point set of T is denoted by F(T) := {x ∈ D(T) : x ∈ Tx}
The study of fixed points for multi-valued nonexpansive mappings using Hausdorff metric was introduced by Markin [ ], and studied extensively by Nadler [ ]
Summary
Let H be a real Hilbert space, CB(H) denote the collection of nonempty, closed, and bounded subsets of H. The class of multi-valued pseudo-contractive mappings introduced by Chidume et al [ ] is as follows. M} of multi-valued ki-strictly pseudo-contractive mappings using a Krasnoselskii-type algorithm Chidume and Okpala [ ] introduced the following definition for multi-valued k-strictly pseudo-contractive mappings. M} of generalized ki-strictly pseudo-contractive multi-valued mappings in a real Hilbert space. ([ ]) Let K be a nonempty subset of a real Hilbert space H and T : K → CB(K) be a generalized k-strictly pseudo-contractive multi-valued mapping. M} of generalized ki-strictly pseudocontractive multi-valued mappings and arbitrary sequence {xn} ⊆ K , let. M, let Ti : K → CB(K) be a family of generalized ki-strictly pseudo-contractive multi-valued mappings with ki ∈ ( , ).
Sign-in/Register to view highlights & summary 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 callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
