Convergence Results for Proximal Point Algorithm in Complete Cat(0) Space for Multivalued Mappings

Samir Dashputre; C. Padmavati; Kavita Sakure

doi:10.22342/jims.27.1.899.29-47

Samir Dashputre ⁽¹⁾ , C. Padmavati ⁽²⁾ , Kavita Sakure ⁽³⁾

(1) , India,

(2) , India,

(3) , India

https://doi.org/10.22342/jims.27.1.899.29-47

Issue
VOLUME 27 NUMBER 1 (MARCH 2021)

Submitted
January 24, 2020

Accepted
December 23, 2020

Published
March 31, 2021

Keywords:

CAT(0) spaces, Nearly Lipschitzian mappings, Proximal point algorithm, Delta-convergence.

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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.

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Authors

Samir Dashputre

C. Padmavati

Kavita Sakure

kavitaaage@gmail.com (Primary Contact)

Dashputre, S., Padmavati, C., & Sakure, K. (2021). Convergence Results for Proximal Point Algorithm in Complete Cat(0) Space for Multivalued Mappings. Journal of the Indonesian Mathematical Society, 27(1), 29–47. https://doi.org/10.22342/jims.27.1.899.29-47