In the year 2008, T. Suzuki [J. Math. Anal. Appl. 340, No. 2, 1088–1095 (2008; Zbl 1140.47041)] showed the following:
Let be a mapping on a subset of a Banach space . Then is said to satify condition (C) if
for all . In this paper, the authors apply this to the solution of the problem for commuting pairs consisting of a single valued mapping and a multivalued mapping in CAT(0) spaces. For this a multivalued version of condition (C) in CAT(0) spaces has been defined.
In this way the authors improve and extend the results of N. Shahzad and J. Markin, in [J. Math. Anal. Appl. 337, No. 2, 1457–1464 (2008; Zbl 1137.47043)].