Common Attractive Points of Generalized Hybrid Multi-Valued Mappings and Applications

Lili Chen, Ni Yang and Jing Zhou
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Lili Chen: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
Ni Yang: Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China
Jing Zhou: School of Mathematics Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China

Mathematics, 2020, vol. 8, issue 8, 1-15

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 ( C A f , g ) and the set of all the common strongly attractive points ( C s A f , 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 A f , F f and C A f , 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.

Keywords: generalized hybrid set-valued mapping; common attractive point; CAT(0) space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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