Abstract
In this paper, we propose the modified proximal point algorithm with the process for three nearly Lipschitzian asymptotically nonexpansive mappings and multivalued mappings in CAT(0) space under certain conditions. We prove some convergence theorems for the algorithm which was introduced by Shamshad Hussain et al. [18]. A numerical example is given to illustrate the efficiency of proximal point algorithm for supporting our result.
Highlights
The proximal point algorithm (PPA) is a method for finding a minimizers of convex lower semicontinuous function defined on Hilbert spaces was initiated by Martinet [29] in 1970
Shimizu et al [39] proved the existence of fixed points for multivalued nonexpansive mappings in convex metric space was established by Shimizu et al [39], i.e. he proved that every multivalued mapping T : Y → C(Y ) has a fixed point in a bounded, complete and uniformly convex metric space (Y, d), where C(Y ) is family of all compact subsets of Y
In the view of above literature, we propose the modified proximal point algorithm with the process for three nearly Lipschitzian asymptotically nonexpansive mappings and multivalued mappings in CAT(0) space under certain conditions
Summary
The proximal point algorithm (PPA) is a method for finding a minimizers of convex lower semicontinuous (lsc) function defined on Hilbert spaces was initiated by Martinet [29] in 1970. Shimizu et al [39] proved the existence of fixed points for multivalued nonexpansive mappings in convex metric space was established by Shimizu et al [39], i.e. he proved that every multivalued mapping T : Y → C(Y ) has a fixed point in a bounded, complete and uniformly convex metric space (Y, d), where C(Y ) is family of all compact subsets of Y In this direction to generalize the nonlinear multivalued mappings, Kim et al [26] introduced the nearly Lipschitzian multivalued mapping. In 2019, Hussain et al [22] has been introduced modified proximal point algorithm in complete CAT(0) space (Y, d) as follows : suppose that h is a convex, proper and lower semi-continuous function on Y. In the view of above literature, we propose the modified proximal point algorithm with the process for three nearly Lipschitzian asymptotically nonexpansive mappings and multivalued mappings in CAT(0) space under certain conditions. A numerical example is given to illustrate the efficiency of proximal point algorithm for supporting our result
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.
