Generalized implicit viscosity approximation method for multivalued mappings in CAT(0) spaces

Demonstratio mathematica

article

Mujahid Abbas¹  Hira Iqbal³  Manuel de la Sen⁴ 

[1] Department of Mathematics, Government College University;Department of Mathematics and Applied Mathematics, University of Pretoria;Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore Campus;Institute of Research and Development of Processes, University of the Basque Country, Campus of Leioa (Bizkaia) - P.O. Box 644- Bilbao

关键词: viscosity approximation method;    variational inequality;    multivalued nonexpansive mapping;    CAT(0) space;   

DOI  :  10.1515/dema-2019-0031

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

We prove strong convergence of the sequence generated by implicit viscosity approximation method involving a multivalued nonexpansive mapping in framework of CAT(0) space. Under certain appropriate conditions on parameters, we show that such a sequence converges strongly to a fixed point of the mapping which solves a variational inequality. We also present some convergence results for the implicit viscosity approximation method in complete ℝ-trees without the endpoint condition.

【 授权许可】

CC BY