Journal of Prime Research in Mathematics

# Fixed Point Approximations of a Family of α-nonexpansive Mappings in CAT(0) Spaces

Sundus Shahzeen$$^{a,*}$$, Maqbool Ahmed$$^a$$, Liliana Guran$$^b$$
$$^a$$ Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan.
$$^b$$ Vasile Goldis” Western University of Arad, Romania.
Correspondence should be addressed to: sundas_shahzeen@outlook.com

### Abstract

In this article, the results deal with the strong convergence of Halpern iteration in CAT(0) spaces. The study revolves around finding a fixed point for nonexpansive mappings, which are also the metric projection points in CA(0) space.Moreover, the strong convergence of Halpern iteration for α-nonexpansive mapping sequence is also given.Our results extend some known results which appeared in the literature.

#### Keywords:

CAT(0) space, Common Fixed Points, Halpern iteration, Semigroups.