Abstract
In this paper, we first propose the concepts of (ζ,η,λ,π)-generalized hybrid multi-valued mappings, the set of all the common attractive points (CAf,g) and the set of all the common strongly attractive points (CsAf,g), respectively for the multi-valued mappings f and g in a CAT(0) space. Moreover, we give some elementary properties in regard to the sets Af, Ff and CAf,g for the multi-valued mappings f and g in a complete CAT(0) space. Furthermore, we present a weak convergence theorem of common attractive points for two (ζ,η,λ,π)-generalized hybrid multi-valued mappings in the above space by virtue of Banach limits technique and Ishikawa iteration respectively. Finally, we prove strong convergence of a new viscosity approximation method for two (ζ,η,λ,π)-generalized hybrid multi-valued mappings in CAT(0) spaces, which also solves a kind of variational inequality problem.
Highlights
In 1975, Baillon proved the first nonlinear ergodic theorem in a Hilbert space
Let Ff be the set of all fixed points of the mapping f
We show the existence of common attractive points for two (ζ, η, λ, π )-generalized hybrid multi-valued mappings by Ishikawa iterative process in a CAT(0) space
Summary
In 1975, Baillon proved the first nonlinear ergodic theorem in a Hilbert space. In 1978, Reich obtained the almost convergence and nonlinear ergodic theorems. They obtained some fundamental properties for attractive points in a real Hilbert space Using these properties, they proved a mean convergence theorem without convexity for finding an attractive point of a generalized hybrid mapping. In 2017, Lili Chen et al [14] raised the definitions of (ζ, η)-generalized hybrid multi-valued mappings in Banach spaces By the way, they gave the concepts of attractive points and strongly attractive points of (ζ, η)-generalized hybrid multi-valued mappings. In 2019, Lili Chen et al [15] introduced the concepts of (ζ, η )-generalized hybrid multi-valued mappings and the corresponding definitions of common attractive points and common strongly attractive points in Hilbert spaces. We obtain a weak convergence theorem of common attractive points for two (ζ, η, λ, π )-generalized hybrid multi-valued mappings in the above space by means of Banach limits technique and Ishikawa iteration respectively. We give a strong convergence theorem of two (ζ, η, λ, π )-generalized hybrid multi-valued mappings by the use of a new viscosity approximation method in CAT(0) spaces, which resolves a kind of variational inequality problem
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
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.
